transversal_oscillation_animation.ipynb

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     },
     "metadata": {},
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    }
   ],
   "source": [
    "# import libraries etc\n",
    "import numpy as np\n",
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure, ColumnDataSource\n",
    "from bokeh.models import CustomJS, Slider, Range1d, Span, Toggle, Spinner\n",
    "from bokeh.layouts import column, row\n",
    "output_notebook()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "93c0df80",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-02T17:02:11.111065Z",
     "start_time": "2022-03-02T17:02:11.104857Z"
    },
    "code_folding": [
     0,
     5
    ]
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   "outputs": [],
   "source": [
    "# setup plot styles\n",
    "colors = ['#000000', '#E69F00', '#56B4E9', '#009E73', '#F0E442', '#0072B2', '#D55E00', '#CC79A7']\n",
    "SUB = str.maketrans(\"0123456789\", \"₀₁₂₃₄₅₆₇₈₉\")\n",
    "SUP = str.maketrans(\"0123456789\", \"⁰¹²³⁴⁵⁶⁷⁸⁹\")\n",
    "\n",
    "def set_fig_style(fig,xmax,ymax,xlab=\"x/l₀\",ylab=\"q(x,t)\",xmin=0,ymin=None):\n",
    "    if ymin is None:\n",
    "        ymin = -ymax\n",
    "    for (ax, lab) in [(fig.xaxis,xlab),(fig.yaxis,ylab)]:\n",
    "        ax.axis_label = lab\n",
    "        ax.axis_label_text_font_size = '14pt'\n",
    "        ax.axis_label_text_font_style = 'normal'\n",
    "        ax.major_label_text_font_size = '12pt'\n",
    "    fig.x_range = Range1d(xmin,xmax)\n",
    "    fig.y_range = Range1d(ymin,ymax)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b625578f",
   "metadata": {},
   "source": [
    "# Transversal modes of an infinite chain of oscillators\n",
    "We here implement and animate the solutions to the normal modes of the transverse oscillations of an infinite chain of masses connected by springs. The normal modes are $e^{i (k x - \\omega(k) t)}$ with frequency $\\omega(k) = \\omega_c \\left|\\sin \\frac{k l_0}{2}\\right|$, with $k \\in \\left(-\\frac{\\pi}{l_0},\\frac{\\pi}{l_0}\\right]$ and $\\omega_c = 2\\sqrt{\\frac{k_s}{m}\\left(1-\\frac{l_n}{l_0}\\right)}$. Here, $k_s$ is the spring constant, $l_n$ is their natural length, and $l_0$ is the distance between the masses (the tension in the chain is $T = k_s (l_0 - l_n)$.) Below, we assume that $\\omega_c = 1$, which is equivalent to choosing the unit of time as $t_c = 1/\\omega_c$ (i.e., the period of oscillation for frequency $\\omega_c$ is $2\\pi$ time units). We could also use $l_0$ as the unit of distance, such that $l_0=1$. While we set it to this value globally, we will keep $l_0$ in the formulas for clarity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ad08755b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-02T17:02:12.012074Z",
     "start_time": "2022-03-02T17:02:12.008924Z"
    }
   },
   "outputs": [],
   "source": [
    "l0 = 1.\n",
    "# for most plots, use x=[0,25] as the plotting range\n",
    "xmax = 25"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b09935c",
   "metadata": {},
   "source": [
    "Plot dispersion relation $\\omega(k)$ and phase velocity $v_f = \\frac{\\omega(k)}{k}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "13dd6084",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-02T17:02:12.843026Z",
     "start_time": "2022-03-02T17:02:12.736942Z"
    },
    "code_folding": [
     0
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"861e3f4c-291b-4da3-a30b-8ad2f42f54d5\" data-root-id=\"1003\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
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       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
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      "application/vnd.bokehjs_exec.v0+json": ""
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     "metadata": {
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       "id": "1003"
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     "output_type": "display_data"
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   ],
   "source": [
    "# plot dispersion and phase velocity\n",
    "\n",
    "# plot positive and negative parts separately to avoid undefined vf at k=0\n",
    "kps = np.linspace(1e-14,np.pi/l0,100)\n",
    "ωs = np.abs(np.sin(kps*l0/2))\n",
    "fig = figure(width=500,height=350)\n",
    "set_fig_style(fig,xmin=-np.pi,xmax=np.pi,ymin=-0.53,ymax=1.03,xlab='k',ylab='')\n",
    "for ks in kps,-kps:\n",
    "    fig.line(ks,ωs,line_width=4,color=colors[0],legend_label='ω(k)')\n",
    "    fig.line(ks,ωs/ks,line_width=3,color=colors[1],legend_label='vf(k)')\n",
    "fig.legend.location = 'bottom_right'\n",
    "fig.title = 'l₀ = 1'\n",
    "show(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa3017f9",
   "metadata": {},
   "source": [
    "Show the oscillators along a chain (black dots), the springs (black lines), and the underlying mode function (orange line). The slider for $k$ controls the wave number within the range $(-\\pi/l_0,\\pi/l_0]$. The vertical dashed orange lines show the position of the maxima of the wave. Note that the range of the slider for $t$ automatically changes so that it ranges from $0$ to $T = \\frac{2\\pi}{\\omega(k)}$, i.e., covers exactly one period of oscillation. Press the `► Play` button to animate the wave propagation.\n",
    "\n",
    "Note that each mass only oscillates up and down, but the overall wave propagates to the left or right depending on the sign of $k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4faf6fda",
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    "ExecuteTime": {
     "end_time": "2022-03-02T17:02:14.449992Z",
     "start_time": "2022-03-02T17:02:14.273790Z"
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    "code_folding": [
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    "scrolled": false
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   "outputs": [
    {
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       "  const render_items = [{\"docid\":\"d6c2b18b-9f1c-447c-b5bc-168e7374a64a\",\"root_ids\":[\"1289\"],\"roots\":{\"1289\":\"6b94bd57-6e2b-4d50-a183-89c1c596105b\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
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       "id": "1289"
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     "output_type": "display_data"
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   "source": [
    "# animate single mode motion\n",
    "def make_mode_animation():\n",
    "    xm = np.arange(0,xmax+1e-8,l0)\n",
    "    x  = np.arange(0,xmax+1e-8,l0/20)\n",
    "\n",
    "    krel0 = 0.2\n",
    "    k0 = krel0*np.pi/l0\n",
    "    source_x = ColumnDataSource(data=dict(x=x, y=np.cos(k0*x)))\n",
    "    source_xm = ColumnDataSource(data=dict(x=xm, y=np.cos(k0*xm)))\n",
    "\n",
    "    fig = figure(width=900,height=500)\n",
    "    fig.line('x','y',source=source_x,line_width=2,color=colors[1])\n",
    "    fig.line('x','y',source=source_xm,line_width=0.5,color=colors[0])\n",
    "    fig.circle('x','y',source=source_xm,size=6,color=colors[0])\n",
    "    # max number of maxima: xmax / λmin = xmax / (2π/kmax) = xmax / (2π/(π/l₀)) = xmax / (2 l₀)\n",
    "    sps = [Span(location=ii*2*np.pi/k0, dimension='height', \n",
    "                line_color=colors[1], line_width=1.5,line_dash=[6,4]) for ii in range(int(xmax/(2*l0))+1)]\n",
    "    fig.renderers.extend(sps)\n",
    "\n",
    "    set_fig_style(fig,xmax,1.2)\n",
    "\n",
    "    slider_k = Slider(start=-1, end=1, value=krel0, step=0.01, title=\"k [π/l₀]\")\n",
    "    slider_t = Slider(start=0, end=20, value=0, step=0.01, title=\"t\", sizing_mode=\"stretch_both\")\n",
    "\n",
    "    # JavaScript callback to do animations directly in the browser (without needing to communicate with server)\n",
    "    cb_sliders = CustomJS(args=dict(sources=[source_x,source_xm], slider_k=slider_k,\n",
    "                                    slider_t=slider_t, sps=sps, l0=l0),\n",
    "                          code=\"\"\"const t = slider_t.value;\n",
    "                                  const k = slider_k.value*Math.PI/l0;\n",
    "                                  const omega = Math.abs(Math.sin(k*l0/2));\n",
    "                                  slider_t.end = omega == 0 ? 100. : 2*Math.PI/omega;\n",
    "                                  sources.forEach(source => {\n",
    "                                      const ys = source.data['y'];\n",
    "                                      source.data['x'].forEach((x,i) => ys[i] = Math.cos(k*x - omega*t));\n",
    "                                      source.change.emit();\n",
    "                                  })\n",
    "                                  const vf = (k==0 ? 0. : omega/k);\n",
    "                                  const λ = 2*Math.PI/Math.abs(k);\n",
    "                                  sps.forEach((sp,i) => sp.location = vf*t + (i+(vf<0))*λ)\"\"\")\n",
    "    for slider in [slider_k,slider_t]:\n",
    "        slider.js_on_change('value', cb_sliders)\n",
    "\n",
    "    # Set up Play/Pause button/toggle JS\n",
    "    cb_toggle = CustomJS(args=dict(s_t=slider_t),\n",
    "                         code=\"\"\"function upfun() { s_t.value = (s_t.value + 0.1) % s_t.end; cb_obj.active || clearInterval(updater) }\n",
    "                                 cb_obj.label = cb_obj.active ? '❚❚ Pause' : '► Play';\n",
    "                                 if (cb_obj.active) var updater = setInterval(upfun, 20);\"\"\")\n",
    "    toggle = Toggle(label='► Play',active=False, sizing_mode=\"stretch_height\", width=80)\n",
    "    toggle.js_on_change('active', cb_toggle)\n",
    "\n",
    "    layout = column(slider_k,row(toggle,slider_t),fig)\n",
    "    \n",
    "    show(layout)\n",
    "\n",
    "make_mode_animation()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "012ebcf9",
   "metadata": {},
   "source": [
    "Show two modes (black and orange lines). Notice, e.g., that waves with smaller $k$ have larger phase velocity $v_f$ since the absolute value of $v_f = \\frac{\\omega(k)}{k} = \\frac{|\\sin(k l_0/2)|}{k}$ decreases with $|k|$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c7ae2454",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-02T17:02:15.946870Z",
     "start_time": "2022-03-02T17:02:15.834111Z"
    },
    "code_folding": [
     0,
     1
    ],
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"4024d53d-f56d-4f7b-b124-b9262a2c4340\" data-root-id=\"1463\"></div>\n"
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\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[501]}},\"selected\":{\"id\":\"1502\"},\"selection_policy\":{\"id\":\"1501\"}},\"id\":\"1384\",\"type\":\"ColumnDataSource\"},{\"attributes\":{},\"id\":\"1407\",\"type\":\"HelpTool\"},{\"attributes\":{},\"id\":\"1392\",\"type\":\"LinearScale\"}],\"root_ids\":[\"1463\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
       "  const render_items = [{\"docid\":\"aefef422-9123-45ae-9e42-59c862f2a003\",\"root_ids\":[\"1463\"],\"roots\":{\"1463\":\"4024d53d-f56d-4f7b-b124-b9262a2c4340\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1463"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# animate motion of two modes\n",
    "def make_two_mode_animation():\n",
    "    x = np.arange(0,xmax+1e-8,l0/20)\n",
    "\n",
    "    krel0s = np.r_[0.1,0.73]\n",
    "    k0s = krel0s*np.pi/l0\n",
    "    source = ColumnDataSource(data = dict(x=x) | {f'y{ik}':np.cos(k*x) for ik,k in enumerate(k0s)})\n",
    "\n",
    "    fig = figure(width=900,height=500)\n",
    "    spcol = []\n",
    "    for ik,k0 in enumerate(k0s):\n",
    "        fig.line('x',f'y{ik}',source=source, line_width=2, color=colors[ik])\n",
    "        sps = [Span(location=ii*2*np.pi/k0,dimension='height',line_color=colors[ik],line_width=1,line_dash=[6,4]) for ii in range(int(xmax/(2*l0))+1)]\n",
    "        fig.renderers.extend(sps)\n",
    "        spcol.append(sps)\n",
    "\n",
    "    set_fig_style(fig,xmax,1.2)\n",
    "\n",
    "    sliders_k = [Slider(start=-1, end=1, value=krel0, step=0.01, title=\"k [π/l₀]\") for krel0 in krel0s]\n",
    "    slider_t = Slider(start=0, end=1000, value=0, step=0.1, title='t', sizing_mode=\"stretch_both\")\n",
    "\n",
    "    # JavaScript callback to do animations directly in the browser (without needing to communicate with server)\n",
    "    cb_sliders = CustomJS(args=dict(source=source, slider_t=slider_t, sliders_k=sliders_k, spcol=spcol, l0=l0),\n",
    "                          code=\"\"\"const t = slider_t.value;\n",
    "                                  const xs = source.data['x'];\n",
    "                                  for (var ik=0; ik<sliders_k.length; ik++) {\n",
    "                                      var ys = source.data[`y${ik}`];\n",
    "                                      var k = sliders_k[ik].value*Math.PI/l0;\n",
    "                                      var omega = Math.abs(Math.sin(k*l0/2));\n",
    "                                      xs.forEach((x,i) => ys[i] = Math.cos(k*x - omega*t));\n",
    "                                      if (k != 0) {\n",
    "                                          const vf = omega/k;\n",
    "                                          const λ = 2*Math.PI/Math.abs(k);\n",
    "                                          const tint = t % (2*Math.PI/omega);\n",
    "                                          spcol[ik].forEach((sp,i) => sp.location = vf*tint + (i+(vf<0))*λ)\n",
    "                                       } else {\n",
    "                                          spcol[ik].forEach(sp => sp.location = 0)\n",
    "                                       }\n",
    "                                   }\n",
    "                                   source.change.emit();\"\"\")\n",
    "    for slider in sliders_k + [slider_t]:\n",
    "        slider.js_on_change('value', cb_sliders)\n",
    "\n",
    "    # Set up Play/Pause button/toggle JS\n",
    "    cb_toggle = CustomJS(args=dict(s_t=slider_t),\n",
    "                         code=\"\"\"function upfun() { s_t.value = (s_t.value + 0.1) % s_t.end; cb_obj.active || clearInterval(updater) }\n",
    "                                 cb_obj.label = cb_obj.active ? '❚❚ Pause' : '► Play';\n",
    "                                 if (cb_obj.active) var updater = setInterval(upfun, 20);\"\"\")\n",
    "    toggle = Toggle(label='► Play',active=False, sizing_mode=\"stretch_height\", width=80)\n",
    "    toggle.js_on_change('active', cb_toggle)\n",
    "\n",
    "    layout = column(*sliders_k,row(toggle,slider_t),fig)\n",
    "    \n",
    "    show(layout)\n",
    "\n",
    "make_two_mode_animation()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f39ca795",
   "metadata": {},
   "source": [
    "Plot a solution consisting of $n$ normal modes. To change from 2 to more modes, add additional entries to the list used for calling the function `make_n_mode_sum_animation`. The list contains the initial values for the sliders $k_i$. The sum over all normal modes is shown in black, with each contributing mode shown as a semi-transparent line. Change the value of the `δt` spinner to change the speed of the animation, and use the `xmax` slider to change the range of values $x$ that is plotted.\n",
    "\n",
    "Some suggestions for values of the different ks: $[0.3,0.32]$, $[0.2,0.4]$, $[0.1,0.2,0.3]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cfb120c6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-02-21T09:15:03.143193Z",
     "start_time": "2022-02-21T09:15:02.948010Z"
    },
    "code_folding": [
     0
    ],
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"4fd39ad0-5358-450e-b48f-c7b3eee70be5\" data-root-id=\"1625\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
       "    \n",
       "  const docs_json = 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\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[2000]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[2000]}},\"selected\":{\"id\":\"1676\"},\"selection_policy\":{\"id\":\"1675\"}},\"id\":\"1559\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"args\":{\"s_dt\":{\"id\":\"1618\"},\"s_t\":{\"id\":\"1616\"}},\"code\":\"function upfun() { s_t.value += s_dt.value; cb_obj.active || clearInterval(updater) }\\n                                 cb_obj.label = cb_obj.active ? '\\u275a\\u275a Pause' : '\\u25ba Play';\\n                                 if (cb_obj.active) var updater = setInterval(upfun, 20);\"},\"id\":\"1620\",\"type\":\"CustomJS\"},{\"attributes\":{\"end\":1,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1619\"}]},\"sizing_mode\":\"stretch_both\",\"start\":-1,\"step\":0.01,\"title\":\"k\\u2082 [\\u03c0/l\\u2080]\",\"value\":0.32},\"id\":\"1613\",\"type\":\"Slider\"},{\"attributes\":{\"source\":{\"id\":\"1559\"}},\"id\":\"1596\",\"type\":\"CDSView\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1583\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"args\":{\"fig\":{\"id\":\"1560\"},\"l0\":1.0,\"slider_t\":{\"id\":\"1616\"},\"slider_xmax\":{\"id\":\"1617\"},\"sliders_c\":[{\"id\":\"1614\"},{\"id\":\"1615\"}],\"sliders_k\":[{\"id\":\"1612\"},{\"id\":\"1613\"}],\"source\":{\"id\":\"1559\"}},\"code\":\"const t = slider_t.value;\\n                                  const xmax = slider_xmax.value;\\n                                  fig.x_range.end = xmax;\\n                                  const xs = source.data['x'];\\n                                  const ys = source.data['y'];\\n                                  const nx = xs.length;\\n                                  xs.forEach((_,i) => { xs[i] = i*xmax/(nx-1); ys[i] = 0 });\\n                                  for (var ik=0; ik<sliders_k.length; ik++) {\\n                                      var yk = source.data[`y${ik}`];\\n                                      var k = sliders_k[ik].value*Math.PI/l0;\\n                                      var c = sliders_c[ik].value;\\n                                      var omega = Math.abs(Math.sin(k*l0/2));\\n                                      xs.forEach((x,i) => { yk[i] = c * Math.cos(k*x - omega*t);\\n                                                            ys[i] += yk[i]; })\\n                                  }\\n                                  source.change.emit();\"},\"id\":\"1619\",\"type\":\"CustomJS\"},{\"attributes\":{\"end\":1,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1619\"}]},\"sizing_mode\":\"stretch_both\",\"start\":0,\"step\":0.01,\"title\":\"c\\u2081\",\"value\":1},\"id\":\"1614\",\"type\":\"Slider\"},{\"attributes\":{\"end\":300,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1619\"}]},\"sizing_mode\":\"stretch_both\",\"start\":25,\"title\":\"xmax\",\"value\":200},\"id\":\"1617\",\"type\":\"Slider\"},{\"attributes\":{},\"id\":\"1578\",\"type\":\"WheelZoomTool\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"#56B4E9\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y1\"}},\"id\":\"1606\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1670\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1582\",\"type\":\"HelpTool\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#E69F00\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y0\"}},\"id\":\"1598\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.5,\"line_color\":\"#56B4E9\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y1\"}},\"id\":\"1604\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1577\",\"type\":\"PanTool\"},{\"attributes\":{\"overlay\":{\"id\":\"1583\"}},\"id\":\"1579\",\"type\":\"BoxZoomTool\"},{\"attributes\":{\"icon\":null,\"js_property_callbacks\":{\"change:active\":[{\"id\":\"1620\"}]},\"label\":\"\\u25ba Play\",\"sizing_mode\":\"stretch_height\",\"width\":80},\"id\":\"1621\",\"type\":\"Toggle\"},{\"attributes\":{},\"id\":\"1671\",\"type\":\"AllLabels\"},{\"attributes\":{},\"id\":\"1580\",\"type\":\"SaveTool\"},{\"attributes\":{\"axis_label\":\"x/l\\u2080\",\"axis_label_text_font_size\":\"14pt\",\"axis_label_text_font_style\":\"normal\",\"coordinates\":null,\"formatter\":{\"id\":\"1673\"},\"group\":null,\"major_label_policy\":{\"id\":\"1674\"},\"major_label_text_font_size\":\"12pt\",\"ticker\":{\"id\":\"1570\"}},\"id\":\"1569\",\"type\":\"LinearAxis\"},{\"attributes\":{\"source\":{\"id\":\"1559\"}},\"id\":\"1602\",\"type\":\"CDSView\"},{\"attributes\":{},\"id\":\"1673\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1574\",\"type\":\"BasicTicker\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#56B4E9\",\"line_width\":2,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y1\"}},\"id\":\"1605\",\"type\":\"Line\"},{\"attributes\":{},\"id\":\"1666\",\"type\":\"DataRange1d\"},{\"attributes\":{\"coordinates\":null,\"group\":null},\"id\":\"1667\",\"type\":\"Title\"},{\"attributes\":{\"children\":[{\"id\":\"1613\"},{\"id\":\"1615\"}],\"sizing_mode\":\"stretch_both\"},\"id\":\"1623\",\"type\":\"Row\"},{\"attributes\":{},\"id\":\"1674\",\"type\":\"AllLabels\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1559\"},\"glyph\":{\"id\":\"1598\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1600\"},\"nonselection_glyph\":{\"id\":\"1599\"},\"view\":{\"id\":\"1602\"}},\"id\":\"1601\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"1581\",\"type\":\"ResetTool\"},{\"attributes\":{\"tools\":[{\"id\":\"1577\"},{\"id\":\"1578\"},{\"id\":\"1579\"},{\"id\":\"1580\"},{\"id\":\"1581\"},{\"id\":\"1582\"}]},\"id\":\"1584\",\"type\":\"Toolbar\"},{\"attributes\":{\"axis\":{\"id\":\"1573\"},\"coordinates\":null,\"dimension\":1,\"group\":null,\"ticker\":null},\"id\":\"1576\",\"type\":\"Grid\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"#000000\",\"line_width\":4,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1594\",\"type\":\"Line\"},{\"attributes\":{\"axis_label\":\"q(x,t)\",\"axis_label_text_font_size\":\"14pt\",\"axis_label_text_font_style\":\"normal\",\"coordinates\":null,\"formatter\":{\"id\":\"1670\"},\"group\":null,\"major_label_policy\":{\"id\":\"1671\"},\"major_label_text_font_size\":\"12pt\",\"ticker\":{\"id\":\"1574\"}},\"id\":\"1573\",\"type\":\"LinearAxis\"}],\"root_ids\":[\"1625\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
       "  const render_items = [{\"docid\":\"0e04a093-56a4-48c5-a4f2-a8285068d885\",\"root_ids\":[\"1625\"],\"roots\":{\"1625\":\"4fd39ad0-5358-450e-b48f-c7b3eee70be5\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
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   "source": [
    "def make_n_mode_sum_animation(krel0s,cs=None,xmax=200):\n",
    "    krel0s = np.asarray(krel0s)\n",
    "    cs = np.ones_like(krel0s) if cs is None else np.asarray(cs)\n",
    "    assert krel0s.ndim == 1\n",
    "    assert krel0s.shape == cs.shape\n",
    "\n",
    "    k0s = krel0s*np.pi/l0\n",
    "    x = np.linspace(0,xmax+1e-8,2000)\n",
    "    source = ColumnDataSource(data = dict(x=x) | {f'y{ik}':np.cos(k*x) for ik,k in enumerate(k0s)})\n",
    "    source.data['y'] = np.sum([source.data[f'y{ik}'] for ik,k in enumerate(k0s)],axis=0)\n",
    "\n",
    "    fig = figure(width=900,height=500)\n",
    "    fig.line('x','y',source=source, line_width=4, color=colors[0])\n",
    "    for ik,k0 in enumerate(k0s):\n",
    "        fig.line('x',f'y{ik}',source=source, line_width=2, line_alpha=0.5, color=colors[(ik+1)%len(colors)])\n",
    "\n",
    "    set_fig_style(fig,xmax,1.2)\n",
    "    del fig.y_range\n",
    "\n",
    "    sliders_k = [Slider(start=-1, end=1, value=krel0, step=0.01, title=f\"k{ik+1} [π/l₀]\".translate(SUB)) for ik,krel0 in enumerate(krel0s)]\n",
    "    sliders_c = [Slider(start=0,  end=1, value=1,     step=0.01, title=f\"c{ik+1}\".translate(SUB))        for ik,krel0 in enumerate(krel0s)]\n",
    "    slider_t = Slider(start=0, end=1000, value=0, step=0.1, title='t', sizing_mode=\"stretch_both\")\n",
    "    slider_xmax = Slider(start=25, end=300, value=xmax, step=1, title='xmax', sizing_mode=\"stretch_both\")\n",
    "    spinner_dt = Spinner(low=0.05, high=5., step=0.05, value=0.1, title=\"δt\", width=80, sizing_mode=\"stretch_height\")\n",
    "\n",
    "    # JavaScript callback to do animations directly in the browser (without needing to communicate with server)\n",
    "    cb_sliders = CustomJS(args=dict(source=source, slider_t=slider_t, slider_xmax=slider_xmax,\n",
    "                                    sliders_k=sliders_k, sliders_c=sliders_c, l0=l0, fig=fig),\n",
    "                          code=\"\"\"const t = slider_t.value;\n",
    "                                  const xmax = slider_xmax.value;\n",
    "                                  fig.x_range.end = xmax;\n",
    "                                  const xs = source.data['x'];\n",
    "                                  const ys = source.data['y'];\n",
    "                                  const nx = xs.length;\n",
    "                                  xs.forEach((_,i) => { xs[i] = i*xmax/(nx-1); ys[i] = 0 });\n",
    "                                  for (var ik=0; ik<sliders_k.length; ik++) {\n",
    "                                      var yk = source.data[`y${ik}`];\n",
    "                                      var k = sliders_k[ik].value*Math.PI/l0;\n",
    "                                      var c = sliders_c[ik].value;\n",
    "                                      var omega = Math.abs(Math.sin(k*l0/2));\n",
    "                                      xs.forEach((x,i) => { yk[i] = c * Math.cos(k*x - omega*t);\n",
    "                                                            ys[i] += yk[i]; })\n",
    "                                  }\n",
    "                                  source.change.emit();\"\"\")\n",
    "    for slider in sliders_k + sliders_c + [slider_t,slider_xmax]:\n",
    "        slider.js_on_change('value', cb_sliders)\n",
    "\n",
    "    # Set up Play/Pause button/toggle JS\n",
    "    cb_toggle = CustomJS(args=dict(s_t=slider_t,s_dt=spinner_dt),\n",
    "                         code=\"\"\"function upfun() { s_t.value += s_dt.value; cb_obj.active || clearInterval(updater) }\n",
    "                                 cb_obj.label = cb_obj.active ? '❚❚ Pause' : '► Play';\n",
    "                                 if (cb_obj.active) var updater = setInterval(upfun, 20);\"\"\")\n",
    "    toggle = Toggle(label='► Play',active=False, sizing_mode=\"stretch_height\", width=80)\n",
    "    toggle.js_on_change('active', cb_toggle)\n",
    "\n",
    "    layout = column(*[row(s_k,s_c,sizing_mode=\"stretch_both\") for (s_k,s_c) in zip(sliders_k,sliders_c)],\n",
    "                    row(toggle, spinner_dt, slider_t),\n",
    "                    slider_xmax,\n",
    "                    fig)\n",
    "    show(layout)\n",
    "\n",
    "make_n_mode_sum_animation([0.3,0.32])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0321ac16",
   "metadata": {},
   "source": [
    "Same as above, but do not create sliders for the wave numbers or amplitudes, just use the values passed directly. This is useful to use a superposition of many modes without having 100 sliders, and also allows complex mode amplitudes without needing two sliders. You can also choose to show the separate normal modes by passing `show_modes` (`=True` or `=False`), and show the individual point masses moving with `show_masses` (`=True` or `=False`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ccf37d53",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-02T17:04:40.590542Z",
     "start_time": "2022-03-02T17:04:40.467399Z"
    },
    "code_folding": [
     0
    ],
    "scrolled": false
   },
   "outputs": [
    {
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       "\n",
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'\\u275a\\u275a Pause' : '\\u25ba Play';\\n                                 if (cb_obj.active) var updater = setInterval(upfun, 20);\"},\"id\":\"1620\",\"type\":\"CustomJS\"},{\"attributes\":{\"below\":[{\"id\":\"1569\"}],\"center\":[{\"id\":\"1572\"},{\"id\":\"1576\"}],\"height\":500,\"left\":[{\"id\":\"1573\"}],\"renderers\":[{\"id\":\"1595\"},{\"id\":\"1601\"},{\"id\":\"1607\"},{\"id\":\"1613\"}],\"title\":{\"id\":\"1664\"},\"toolbar\":{\"id\":\"1584\"},\"width\":900,\"x_range\":{\"id\":\"1615\"},\"x_scale\":{\"id\":\"1565\"},\"y_range\":{\"id\":\"1616\"},\"y_scale\":{\"id\":\"1567\"}},\"id\":\"1560\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"axis_label\":\"x/l\\u2080\",\"axis_label_text_font_size\":\"14pt\",\"axis_label_text_font_style\":\"normal\",\"coordinates\":null,\"formatter\":{\"id\":\"1670\"},\"group\":null,\"major_label_policy\":{\"id\":\"1671\"},\"major_label_text_font_size\":\"12pt\",\"ticker\":{\"id\":\"1570\"}},\"id\":\"1569\",\"type\":\"LinearAxis\"},{\"attributes\":{\"args\":{\"acs\":[0.5,1.0,0.5],\"fig\":{\"id\":\"1560\"},\"ks\":[0.9424777960769379,1.0053096491487339,1.0681415022205298],\"l0\":1.0,\"phis\":[0.0,0.0,0.0],\"show_modes\":true,\"slider_t\":{\"id\":\"1617\"},\"sources\":[{\"id\":\"1559\"}]},\"code\":\"const t = slider_t.value;\\n                                  const omegas = ks.map(k => Math.abs(Math.sin(k*l0/2)));\\n                                  sources.forEach((source,isource) => {\\n                                      const xs = source.data['x'];\\n                                      const ys = source.data['y'];\\n                                      const do_modes = show_modes && (isource==0);\\n                                      ys.forEach((_,i) => ys[i] = 0);\\n                                      for (var ik=0; ik<ks.length; ik++) {\\n                                          if (do_modes) { var yk = source.data[`y${ik}`] };\\n                                          const k = ks[ik], omega = omegas[ik], ac = acs[ik], phi = phis[ik];\\n                                          xs.forEach((x,i) => { const ym = ac * Math.cos(k*x - omega*t + phi);\\n                                                                ys[i] += ym;\\n                                                                if (do_modes) yk[i] = ym; })\\n                                      }\\n                                      source.change.emit()\\n                                  })\"},\"id\":\"1619\",\"type\":\"CustomJS\"},{\"attributes\":{\"end\":1000,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1619\"}]},\"sizing_mode\":\"stretch_both\",\"start\":0,\"step\":0.1,\"title\":\"t\",\"value\":0},\"id\":\"1617\",\"type\":\"Slider\"},{\"attributes\":{\"children\":[{\"id\":\"1621\"},{\"id\":\"1618\"},{\"id\":\"1617\"}]},\"id\":\"1622\",\"type\":\"Row\"},{\"attributes\":{\"icon\":null,\"js_property_callbacks\":{\"change:active\":[{\"id\":\"1620\"}]},\"label\":\"\\u25ba 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       "  const render_items = [{\"docid\":\"893b92b2-1d6f-4c99-90ed-32dc79e53c3f\",\"root_ids\":[\"1623\"],\"roots\":{\"1623\":\"c6181fa6-c660-4d4a-af97-250461d4fda3\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
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       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
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      ],
      "application/vnd.bokehjs_exec.v0+json": ""
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     "output_type": "display_data"
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   ],
   "source": [
    "def make_n_mode_sum_animation_nosliders(krels,cs,xmax=200,show_modes=True,show_masses=False,dx=None):\n",
    "    krels = np.asarray(krels)\n",
    "    cs = np.asarray(cs)\n",
    "    assert krels.ndim == 1\n",
    "    assert krels.shape == cs.shape\n",
    "\n",
    "    acs = abs(cs)\n",
    "    phis = np.angle(cs)\n",
    "\n",
    "    def make_source(x,include_modes):\n",
    "        source = ColumnDataSource(data = dict(x=x,y=0*x))\n",
    "        for ik,(k,ac,phi) in enumerate(zip(ks,acs,phis)):\n",
    "            yi = ac*np.cos(k*x+phi)\n",
    "            source.data['y'] += yi\n",
    "            if include_modes:\n",
    "                source.data[f'y{ik}'] = yi\n",
    "        return source\n",
    "    \n",
    "    ks = krels*np.pi/l0\n",
    "    if dx is None:\n",
    "        # resolution: take 40 points per shortest wavelength in the packet\n",
    "        # dx = λmin / 40 = 2π/kmax / 40\n",
    "        dx = 2*np.pi/(40*abs(ks).max())\n",
    "    \n",
    "    sources = [make_source(np.arange(0,xmax,dx), show_modes)]\n",
    "    if show_masses:\n",
    "        sources.append(make_source(np.arange(0,xmax,l0), False))\n",
    "            \n",
    "    fig = figure(width=900,height=500)\n",
    "    fig.line('x','y',source=sources[0], line_width=4, color=colors[0])\n",
    "    if show_modes:\n",
    "        for ik,k in enumerate(ks):\n",
    "            fig.line('x',f'y{ik}',source=sources[0], line_width=2, line_alpha=0.5,\n",
    "                     color=colors[1 + (ik%(len(colors)-1))])\n",
    "    if show_masses:\n",
    "        fig.circle('x','y',source=sources[1],size=6,color=colors[0])\n",
    "            \n",
    "    set_fig_style(fig,xmax,ymax=1.03*abs(sources[0].data['y']).max())\n",
    "\n",
    "    slider_t = Slider(start=0, end=1000, value=0, step=0.1, title='t', sizing_mode=\"stretch_both\")\n",
    "    spinner_dt = Spinner(low=0.05, high=5., step=0.05, value=0.1, title=\"δt\", width=80, sizing_mode=\"stretch_height\")\n",
    "\n",
    "    # JavaScript callback to do animations directly in the browser (without needing to communicate with server)\n",
    "    cb_sliders = CustomJS(args=dict(sources=sources, slider_t=slider_t, ks=ks, acs=acs,\n",
    "                                    phis=phis, l0=l0, fig=fig, show_modes=show_modes),\n",
    "                          code=\"\"\"const t = slider_t.value;\n",
    "                                  const omegas = ks.map(k => Math.abs(Math.sin(k*l0/2)));\n",
    "                                  sources.forEach((source,isource) => {\n",
    "                                      const xs = source.data['x'];\n",
    "                                      const ys = source.data['y'];\n",
    "                                      const do_modes = show_modes && (isource==0);\n",
    "                                      ys.forEach((_,i) => ys[i] = 0);\n",
    "                                      for (var ik=0; ik<ks.length; ik++) {\n",
    "                                          if (do_modes) { var yk = source.data[`y${ik}`] };\n",
    "                                          const k = ks[ik], omega = omegas[ik], ac = acs[ik], phi = phis[ik];\n",
    "                                          xs.forEach((x,i) => { const ym = ac * Math.cos(k*x - omega*t + phi);\n",
    "                                                                ys[i] += ym;\n",
    "                                                                if (do_modes) yk[i] = ym; })\n",
    "                                      }\n",
    "                                      source.change.emit()\n",
    "                                  })\"\"\")\n",
    "    slider_t.js_on_change('value', cb_sliders)\n",
    "\n",
    "    # Set up Play/Pause button/toggle JS\n",
    "    cb_toggle = CustomJS(args=dict(s_t=slider_t,s_dt=spinner_dt),\n",
    "                         code=\"\"\"function upfun() { s_t.value += s_dt.value; cb_obj.active || clearInterval(updater) }\n",
    "                                 cb_obj.label = cb_obj.active ? '❚❚ Pause' : '► Play';\n",
    "                                 if (cb_obj.active) var updater = setInterval(upfun, 20);\"\"\")\n",
    "    toggle = Toggle(label='► Play',active=False, sizing_mode=\"stretch_height\", width=80)\n",
    "    toggle.js_on_change('active', cb_toggle)\n",
    "\n",
    "    layout = column(row(toggle, spinner_dt, slider_t), fig)\n",
    "    show(layout)\n",
    "\n",
    "make_n_mode_sum_animation_nosliders([0.3,0.32,0.34],[0.5,1.,0.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d83a045",
   "metadata": {},
   "source": [
    "Use the code above to create a wavepacket with many components (30 values ranging from $k=0$ to $k=0.3 \\pi/l_0$), with a Gaussian distribution of amplitudes and a complex phase corresponding to a position offset. Notice that during the propagation (set $\\delta t$ to larger values to see it better), the wavepackets slowly change shape. This is because the dispersion relation is not perfectly linear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b667822b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-02T17:04:41.818454Z",
     "start_time": "2022-03-02T17:04:41.571964Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
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       "  const render_items = [{\"docid\":\"845b5af0-f4ca-463c-bf58-ce2fee395ce5\",\"root_ids\":[\"1730\"],\"roots\":{\"1730\":\"38f53b29-82fa-4721-bf14-d35fd4b8ac12\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
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       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
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       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
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       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
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       "  const docs_json = 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\",\"dtype\":\"float64\",\"order\":\"little\",\"shape\":[1800]}},\"selected\":{\"id\":\"2035\"},\"selection_policy\":{\"id\":\"2034\"}},\"id\":\"1914\",\"type\":\"ColumnDataSource\"},{\"attributes\":{\"high\":5.0,\"low\":0.05,\"sizing_mode\":\"stretch_height\",\"step\":0.05,\"title\":\"\\u03b4t\",\"value\":0.1,\"value_throttled\":0.1,\"width\":80},\"id\":\"1955\",\"type\":\"Spinner\"},{\"attributes\":{},\"id\":\"1936\",\"type\":\"ResetTool\"},{\"attributes\":{},\"id\":\"1935\",\"type\":\"SaveTool\"},{\"attributes\":{\"bottom_units\":\"screen\",\"coordinates\":null,\"fill_alpha\":0.5,\"fill_color\":\"lightgrey\",\"group\":null,\"left_units\":\"screen\",\"level\":\"overlay\",\"line_alpha\":1.0,\"line_color\":\"black\",\"line_dash\":[4,4],\"line_width\":2,\"right_units\":\"screen\",\"syncable\":false,\"top_units\":\"screen\"},\"id\":\"1938\",\"type\":\"BoxAnnotation\"},{\"attributes\":{\"end\":1000,\"js_property_callbacks\":{\"change:value\":[{\"id\":\"1956\"}]},\"sizing_mode\":\"stretch_both\",\"start\":0,\"step\":0.1,\"title\":\"t\",\"value\":0},\"id\":\"1954\",\"type\":\"Slider\"},{\"attributes\":{\"args\":{\"s_dt\":{\"id\":\"1955\"},\"s_t\":{\"id\":\"1954\"}},\"code\":\"function upfun() { s_t.value += s_dt.value; cb_obj.active || clearInterval(updater) }\\n                                 cb_obj.label = cb_obj.active ? '\\u275a\\u275a Pause' : '\\u25ba Play';\\n                                 if (cb_obj.active) var updater = setInterval(upfun, 20);\"},\"id\":\"1957\",\"type\":\"CustomJS\"},{\"attributes\":{\"source\":{\"id\":\"1914\"}},\"id\":\"1951\",\"type\":\"CDSView\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"1914\"},\"glyph\":{\"id\":\"1947\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"1949\"},\"nonselection_glyph\":{\"id\":\"1948\"},\"view\":{\"id\":\"1951\"}},\"id\":\"1950\",\"type\":\"GlyphRenderer\"},{\"attributes\":{},\"id\":\"2029\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{},\"id\":\"1920\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"2030\",\"type\":\"AllLabels\"},{\"attributes\":{\"line_color\":\"#000000\",\"line_width\":4,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1947\",\"type\":\"Line\"},{\"attributes\":{\"end\":300},\"id\":\"1952\",\"type\":\"Range1d\"},{\"attributes\":{\"axis\":{\"id\":\"1924\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"1927\",\"type\":\"Grid\"},{\"attributes\":{\"tools\":[{\"id\":\"1932\"},{\"id\":\"1933\"},{\"id\":\"1934\"},{\"id\":\"1935\"},{\"id\":\"1936\"},{\"id\":\"1937\"}]},\"id\":\"1939\",\"type\":\"Toolbar\"},{\"attributes\":{},\"id\":\"2032\",\"type\":\"BasicTickFormatter\"},{\"attributes\":{\"coordinates\":null,\"group\":null},\"id\":\"2026\",\"type\":\"Title\"},{\"attributes\":{\"below\":[{\"id\":\"1924\"}],\"center\":[{\"id\":\"1927\"},{\"id\":\"1931\"}],\"height\":500,\"left\":[{\"id\":\"1928\"}],\"renderers\":[{\"id\":\"1950\"}],\"title\":{\"id\":\"2026\"},\"toolbar\":{\"id\":\"1939\"},\"width\":900,\"x_range\":{\"id\":\"1952\"},\"x_scale\":{\"id\":\"1920\"},\"y_range\":{\"id\":\"1953\"},\"y_scale\":{\"id\":\"1922\"}},\"id\":\"1915\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{},\"id\":\"2033\",\"type\":\"AllLabels\"},{\"attributes\":{\"children\":[{\"id\":\"1958\"},{\"id\":\"1955\"},{\"id\":\"1954\"}]},\"id\":\"1959\",\"type\":\"Row\"},{\"attributes\":{\"end\":7.487297145046722,\"start\":-7.487297145046722},\"id\":\"1953\",\"type\":\"Range1d\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#000000\",\"line_width\":4,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"1948\",\"type\":\"Line\"},{\"attributes\":{\"icon\":null,\"js_property_callbacks\":{\"change:active\":[{\"id\":\"1957\"}]},\"label\":\"\\u25ba Play\",\"sizing_mode\":\"stretch_height\",\"width\":80},\"id\":\"1958\",\"type\":\"Toggle\"},{\"attributes\":{\"args\":{\"acs\":[3.726653172078671e-06,1.9691665140351026e-05,9.238589279517675e-05,0.00038484746544230385,0.0014234143957181377,0.004674485632429255,0.0136300063204185,0.035287268144831546,0.08111473813677472,0.16555460133144137,0.3000146716208581,0.48272910432484045,0.6896428316817934,0.874791836355582,0.9852466549645503,0.9852466549645502,0.874791836355582,0.6896428316817933,0.4827291043248405,0.3000146716208579,0.16555460133144134,0.08111473813677472,0.035287268144831456,0.013630006320418477,0.004674485632429255,0.001423414395718134,0.00038484746544230385,9.238589279517642e-05,1.969166514035092e-05,3.726653172078671e-06],\"fig\":{\"id\":\"1915\"},\"ks\":[0.0,0.032499234347480616,0.06499846869496123,0.09749770304244186,0.12999693738992246,0.16249617173740308,0.19499540608488372,0.22749464043236434,0.2599938747798449,0.2924931091273255,0.32499234347480616,0.3574915778222868,0.38999081216976744,0.42249004651724803,0.4549892808647287,0.4874885152122093,0.5199877495596898,0.5524869839071704,0.584986218254651,0.6174854526021317,0.6499846869496123,0.682483921297093,0.7149831556445736,0.7474823899920542,0.7799816243395349,0.8124808586870155,0.8449800930344961,0.8774793273819768,0.9099785617294573,0.9424777960769379],\"l0\":1.0,\"phis\":[0.0,-1.2999693738992246,-2.5999387477984492,2.3832771854819117,1.083307811582688,-0.21666156231653727,-1.5166309362157626,-2.8166003101149886,2.166615623165376,0.8666462492661525,-0.4333231246330746,-1.7332924985323,-3.0332618724315252,1.9499540608488395,0.649984686949609,-0.649984686949611,-1.9499540608488346,3.033261872431525,1.7332924985323048,0.4333231246330743,-0.8666462492661492,-2.1666156231653764,2.816600310114987,1.5166309362157633,0.2166615623165361,-1.0833078115826837,-2.3832771854819073,2.5999387477984484,1.2999693738992177,1.4695761589768238e-15],\"show_modes\":false,\"slider_t\":{\"id\":\"1954\"},\"sources\":[{\"id\":\"1914\"}]},\"code\":\"const t = slider_t.value;\\n                                  const omegas = ks.map(k => Math.abs(Math.sin(k*l0/2)));\\n                                  sources.forEach((source,isource) => {\\n                                      const xs = source.data['x'];\\n                                      const ys = source.data['y'];\\n                                      const do_modes = show_modes && (isource==0);\\n                                      ys.forEach((_,i) => ys[i] = 0);\\n                                      for (var ik=0; ik<ks.length; ik++) {\\n                                          if (do_modes) { var yk = source.data[`y${ik}`] };\\n                                          const k = ks[ik], omega = omegas[ik], ac = acs[ik], phi = phis[ik];\\n                                          xs.forEach((x,i) => { const ym = ac * Math.cos(k*x - omega*t + phi);\\n                                                                ys[i] += ym;\\n                                                                if (do_modes) yk[i] = ym; })\\n                                      }\\n                                      source.change.emit()\\n                                  })\"},\"id\":\"1956\",\"type\":\"CustomJS\"}],\"root_ids\":[\"1960\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
       "  const render_items = [{\"docid\":\"e0bffff7-0dd1-4b08-805b-e408f91692e0\",\"root_ids\":[\"1960\"],\"roots\":{\"1960\":\"5041ee6a-cec7-4c03-8881-d306978963af\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "1960"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "krels = np.linspace(0.0,0.3,30)\n",
    "cs = np.exp(-(krels-0.15)**2/(2*0.03**2) - 1j*40*krels*np.pi/l0)\n",
    "\n",
    "fig = figure(height=180,width=900)\n",
    "fig.line(krels,abs(cs),line_width=1,color=colors[0])\n",
    "fig.circle(krels,abs(cs),size=7,color=colors[0])\n",
    "set_fig_style(fig,krels[-1]*1.01,1.)\n",
    "del fig.y_range\n",
    "fig.xaxis.axis_label = \"k [π/l₀]\"\n",
    "fig.yaxis.axis_label = \"|c(k)|\"\n",
    "show(fig)\n",
    "\n",
    "make_n_mode_sum_animation_nosliders(krels,cs,xmax=300,show_modes=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dba70e4",
   "metadata": {},
   "source": [
    "## create solutions for finite chains by choosing solutions of the infinite one that satisfy the boundary conditions\n",
    "For example, we assume that the masses at positions $x=0$ and $x=L$ (where $L = m l_0$, with $m>1$ an integer) are fixed at $y=0$, i.e., we have the boundary condition $y(x=0,t) = y(x=L,t) = 0$.\n",
    "\n",
    "We also note that due to the degeneracy $\\omega(k)=\\omega(-k)$, any sum of plane waves with $k$ and $-k$ is also a normal mode, $c_+ e^{i(kx-\\omega t} + c_- e^{i(-kx-\\omega t)} = (c_+ e^{ikx} + c_- e^{-ikx}) e^{-i\\omega t}$. In particular, the choices $c_- = \\pm c_+$ give standing waves, as $e^{i k x} + e^{-i k x} = 2 \\cos(k x)$ and $e^{i k x} - e^{-i k x} = 2i \\sin(k x)$. We can thus use standing cosine and sine waves instead of propagating plane waves as an equally valid normal mode basis. In order to fulfill $y(x=0,t) = 0$, the cosine-modes cannot contribute. Furthermore, in order to fulfill $y(x=L,t)=0$, we need that $\\sin(k L) = 0$, i.e., only the discrete values $k_n =\\frac{n\\pi}{L}$, with $n \\in \\mathbb{N}^+$ are allowed.\n",
    "\n",
    "Note that the normalized `krel` below is $k \\frac{l_0}{\\pi}$, so $k_n =\\frac{n\\pi}{L}$ corresponds to $k_{\\mathrm{rel}} = \\frac{n l_0}{L}$. Since $k_{\\mathrm{rel}} \\in (-1,1]$, $n$ is restricted to a maximum value of $N = \\frac{L}{l_0}$. However, the masses for $n=N$ are exactly at nodes of the sine wave ($\\sin \\frac{L}{l_0} \\frac{\\pi}{L} x = \\sin j \\pi = 0$ for $x=j l_0$), so this mode describes no motion. The highest actual value of $n$ is thus $n_\\max = N-1$. Note that the number of discrete modes that appears is thus exactly the number of free masses, as it should be. Finally, since this is just an alternative way to arrive at the same solution, the frequencies $\\omega_n = \\omega_c |\\sin(k_n l_0/2)|$ are exactly the same as those obtained by diagonalizing the matrices $\\hat{M}$ and $\\hat{K}$ describing the same system, and the eigenvectors (either obtained by evaluating the mode functions at $x=jl_0$ or by diagonalizing the matrices) naturally also agree."
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  {
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   "execution_count": 11,
   "id": "ed4fdad8",
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     "start_time": "2022-03-02T17:04:43.935763Z"
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   },
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      "Number of normal modes: 4\n"
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Application\",\"version\":\"2.4.2\"}};\n",
       "  const render_items = [{\"docid\":\"9414a008-1f73-46cd-81fd-b79c54eba356\",\"root_ids\":[\"2181\"],\"roots\":{\"2181\":\"eea521ac-b7d8-4535-a31a-660444ad554e\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "2181"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 5*l0\n",
    "nmax = int(L/l0 - 0.5)\n",
    "print(\"Number of normal modes:\", nmax)\n",
    "krpos = np.arange(1,nmax+1) * l0/L\n",
    "cpos = np.r_[1.3,0.4,0.2,np.zeros(nmax-3)]\n",
    "krels = np.r_[-krpos[::-1],krpos]\n",
    "# make the complex coefficients -i/2 c_n and i/2 c_n to get real sine waves\n",
    "cs = -0.5j * np.r_[-cpos[::-1],cpos]\n",
    "\n",
    "# only pass the actually nonzero modes\n",
    "inds = np.nonzero(cs)\n",
    "krels = krels[inds]\n",
    "cs = cs[inds]\n",
    "\n",
    "make_n_mode_sum_animation_nosliders(krels,cs,xmax=L+1e-8,show_modes=True,show_masses=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5a4ef942",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-03-02T17:04:46.200054Z",
     "start_time": "2022-03-02T17:04:45.707922Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of normal modes: 799\n",
      "Number of modes with non-zero amplitude: 400\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "  <div class=\"bk-root\" id=\"547b70e1-b9e9-4d3b-bbf8-8ed7014a62fa\" data-root-id=\"2382\"></div>\n"
      ]
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     "metadata": {},
     "output_type": "display_data"
    },
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     "data": {
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t = slider_t.value;\\n                                  const omegas = ks.map(k => Math.abs(Math.sin(k*l0/2)));\\n                                  sources.forEach((source,isource) => {\\n                                      const xs = source.data['x'];\\n                                      const ys = source.data['y'];\\n                                      const do_modes = show_modes && (isource==0);\\n                                      ys.forEach((_,i) => ys[i] = 0);\\n                                      for (var ik=0; ik<ks.length; ik++) {\\n                                          if (do_modes) { var yk = source.data[`y${ik}`] };\\n                                          const k = ks[ik], omega = omegas[ik], ac = acs[ik], phi = phis[ik];\\n                                          xs.forEach((x,i) => { const ym = ac * Math.cos(k*x - omega*t + phi);\\n                                                                ys[i] += ym;\\n                                                                if (do_modes) yk[i] = ym; })\\n                                      }\\n                                      source.change.emit()\\n                                  })\"},\"id\":\"2378\",\"type\":\"CustomJS\"},{\"attributes\":{\"children\":[{\"id\":\"2380\"},{\"id\":\"2377\"},{\"id\":\"2376\"}]},\"id\":\"2381\",\"type\":\"Row\"},{\"attributes\":{\"axis_label\":\"q(x,t)\",\"axis_label_text_font_size\":\"14pt\",\"axis_label_text_font_style\":\"normal\",\"coordinates\":null,\"formatter\":{\"id\":\"2475\"},\"group\":null,\"major_label_policy\":{\"id\":\"2476\"},\"major_label_text_font_size\":\"12pt\",\"ticker\":{\"id\":\"2351\"}},\"id\":\"2350\",\"type\":\"LinearAxis\"},{\"attributes\":{\"args\":{\"s_dt\":{\"id\":\"2377\"},\"s_t\":{\"id\":\"2376\"}},\"code\":\"function upfun() { s_t.value += s_dt.value; cb_obj.active || clearInterval(updater) }\\n                                 cb_obj.label = cb_obj.active ? '\\u275a\\u275a Pause' : '\\u25ba Play';\\n                                 if (cb_obj.active) var updater = setInterval(upfun, 20);\"},\"id\":\"2379\",\"type\":\"CustomJS\"},{\"attributes\":{\"icon\":null,\"js_property_callbacks\":{\"change:active\":[{\"id\":\"2379\"}]},\"label\":\"\\u25ba Play\",\"sizing_mode\":\"stretch_height\",\"width\":80},\"id\":\"2380\",\"type\":\"Toggle\"},{\"attributes\":{},\"id\":\"2342\",\"type\":\"LinearScale\"},{\"attributes\":{},\"id\":\"2347\",\"type\":\"BasicTicker\"},{\"attributes\":{\"coordinates\":null,\"data_source\":{\"id\":\"2336\"},\"glyph\":{\"id\":\"2369\"},\"group\":null,\"hover_glyph\":null,\"muted_glyph\":{\"id\":\"2371\"},\"nonselection_glyph\":{\"id\":\"2370\"},\"view\":{\"id\":\"2373\"}},\"id\":\"2372\",\"type\":\"GlyphRenderer\"},{\"attributes\":{\"coordinates\":null,\"group\":null},\"id\":\"2472\",\"type\":\"Title\"},{\"attributes\":{\"axis\":{\"id\":\"2346\"},\"coordinates\":null,\"group\":null,\"ticker\":null},\"id\":\"2349\",\"type\":\"Grid\"},{\"attributes\":{},\"id\":\"2344\",\"type\":\"LinearScale\"},{\"attributes\":{\"tools\":[{\"id\":\"2354\"},{\"id\":\"2355\"},{\"id\":\"2356\"},{\"id\":\"2357\"},{\"id\":\"2358\"},{\"id\":\"2359\"}]},\"id\":\"2361\",\"type\":\"Toolbar\"},{\"attributes\":{\"below\":[{\"id\":\"2346\"}],\"center\":[{\"id\":\"2349\"},{\"id\":\"2353\"}],\"height\":500,\"left\":[{\"id\":\"2350\"}],\"renderers\":[{\"id\":\"2372\"}],\"title\":{\"id\":\"2472\"},\"toolbar\":{\"id\":\"2361\"},\"width\":900,\"x_range\":{\"id\":\"2374\"},\"x_scale\":{\"id\":\"2342\"},\"y_range\":{\"id\":\"2375\"},\"y_scale\":{\"id\":\"2344\"}},\"id\":\"2337\",\"subtype\":\"Figure\",\"type\":\"Plot\"},{\"attributes\":{\"line_alpha\":0.1,\"line_color\":\"#000000\",\"line_width\":4,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2370\",\"type\":\"Line\"},{\"attributes\":{\"line_alpha\":0.2,\"line_color\":\"#000000\",\"line_width\":4,\"x\":{\"field\":\"x\"},\"y\":{\"field\":\"y\"}},\"id\":\"2371\",\"type\":\"Line\"},{\"attributes\":{\"end\":1.2700678169755417,\"start\":-1.2700678169755417},\"id\":\"2375\",\"type\":\"Range1d\"}],\"root_ids\":[\"2382\"]},\"title\":\"Bokeh Application\",\"version\":\"2.4.2\"}};\n",
       "  const render_items = [{\"docid\":\"3ed3b087-910b-474b-bef4-fa92865dbad9\",\"root_ids\":[\"2382\"],\"roots\":{\"2382\":\"547b70e1-b9e9-4d3b-bbf8-8ed7014a62fa\"}}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
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     "output_type": "display_data"
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   ],
   "source": [
    "L = 800*l0\n",
    "nmax = int(L/l0 - 0.5)\n",
    "print(\"Number of normal modes:\", nmax)\n",
    "ns = np.arange(1,nmax+1)\n",
    "krpos = ns * l0/L\n",
    "cpos = 1/ns**2 * np.sin(ns*np.pi/2)\n",
    "# only pass the actually nonzero modes\n",
    "inds, = np.where(abs(cpos)>1e-7)\n",
    "krpos = krpos[inds]\n",
    "cpos = cpos[inds]\n",
    "print(\"Number of modes with non-zero amplitude:\", len(cpos))\n",
    "\n",
    "krels = np.r_[-krpos[::-1],krpos]\n",
    "# make the complex coefficients -i c_n and i c_n to get real sine waves\n",
    "cs = -0.5j * np.r_[-cpos[::-1],cpos]\n",
    "\n",
    "make_n_mode_sum_animation_nosliders(krels,cs,xmax=L+1e-8,show_modes=False,show_masses=False,dx=l0)"
   ]
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