classes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ffd5c3e2",
   "metadata": {},
   "source": [
    "# Classes / Objects in Python\n",
    "\n",
    "<b>Create a Class</b> <br />\n",
    "To create a class, use the keyword class:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "86b9a55c",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SampleClass:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "30d94ee2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "__main__.SampleClass"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SampleClass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b7460bfe",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SampleClass:\n",
    "    x = 5\n",
    "    y = 10\n",
    "    z = x * y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e9a781eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SampleClass.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fce76d13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SampleClass.z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdacef5e",
   "metadata": {},
   "source": [
    "# Create an object from the Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "43e206c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc = SampleClass()\n",
    "sc.z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c9a2231",
   "metadata": {},
   "source": [
    "# The __init__() Function\n",
    "\n",
    "***Use the __init__() function to assign values to object properties, or other operations that are necessary to do when the object is being created***\n",
    "<br />\n",
    "\n",
    "***Note: The __init__() function is called automatically every time the class is being used to create a new object.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6c672f08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class Area_of_Triangle:\n",
    "  def __init__(self, b, h):\n",
    "    self.b = b\n",
    "    self.h = h\n",
    "\n",
    "\n",
    "area = Area_of_Triangle(5, 10)\n",
    "\n",
    "area.h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e72c6209",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'10'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1 = Area_of_Triangle('5','10')\n",
    "a1.h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "10c07ef3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The area of triangle ABC with height, 10 and base of 5 is 50\n"
     ]
    }
   ],
   "source": [
    "print( f\"The area of triangle ABC with height, {area.h} and base of {area.b} is {area.h*area.b}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a3db38ba",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "53c259d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Circle:\n",
    "    def __init__(self, r):\n",
    "        self.r = r\n",
    "        \n",
    "    def area(self):\n",
    "        print(f\"Area of Circle with radius ({self.r}) = {(22/7)*float(self.r)**2} \")\n",
    "\n",
    "    def circumference(self):\n",
    "        print(f\"Circumference of Circle with radius ({self.r}) = {2*(22/7)*float(self.r)} \")\n",
    "        \n",
    "    def diameter(self):\n",
    "        print(f\"Diameter of Circle with radius ({self.r}) = {2*float(self.r)} \")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "7cdd31a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area of Circle with radius (7) = 154.0 \n",
      "Circumference of Circle with radius (7) = 44.0 \n",
      "Diameter of Circle with radius (7) = 14.0 \n",
      "None None None\n"
     ]
    }
   ],
   "source": [
    "p1 = Circle(r=7)\n",
    "print(p1.area(), p1.circumference(), p1.diameter())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "c03f9f75",
   "metadata": {},
   "outputs": [],
   "source": [
    "p1.r = 21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "9b8ec4e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diameter of Circle with radius (21) = 42.0 \n"
     ]
    }
   ],
   "source": [
    "p1.diameter()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "d8abefc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area of Circle with radius (7) = 154.0 \n",
      "Circumference of Circle with radius (7) = 44.0 \n",
      "Diameter of Circle with radius (7) = 14.0 \n",
      "None None None\n"
     ]
    }
   ],
   "source": [
    "print(p1.area(), p1.circumference(), p1.diameter())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd1a74a7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "92390a31",
   "metadata": {},
   "source": [
    "<h1> Trial Question </h1>\n",
    "<h3> 1-D Harmonic Oscillation </h3>\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Using ***Python classes and numerical methods***, simulate the motion of a one-dimensional harmonic oscillator with a mass of 1 kg, a spring constant of 2 N/m, an initial position of 1 m, and an initial velocity of 0 m/s. \n",
    "\n",
    " - Plot the position and velocity of the oscillator as a function of time for a duration of 10 seconds, using a time step of 0.01 seconds.  <br /><br />\n",
    "\n",
    " - Provide a brief explanation of your implementation and discuss the observed motion based on the plotted results.\n",
    " \n",
    " \n",
    "\n",
    "\n",
    "<br /><br /><br />\n",
    "***Key Expressions (How To)*** <br />\n",
    "In this problem, you are asked to simulate the motion of a one-dimensional harmonic oscillator using the following equation of motion:\n",
    "\n",
    "$$F = -k \\times x$$\n",
    "\n",
    "where F is the restoring force, k is the spring constant, and x is the displacement from the equilibrium position. The force acting on the mass can be related to its acceleration (a) through Newton's second law:\n",
    "\n",
    "$$F = m * a$$\n",
    "\n",
    "where m is the mass of the oscillator. Combining these two equations gives:\n",
    "\n",
    "$$m * a = -k * x$$\n",
    "\n",
    "or\n",
    "\n",
    "$$a = -(k/m) * x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b1730c2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0238f8b",
   "metadata": {},
   "source": [
    "# Build A Class For The Harmonic Oscillation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7f61548e",
   "metadata": {},
   "outputs": [],
   "source": [
    "class HarmonicOscillator:\n",
    "    def __init__(self, mass, spring_constant, initial_position, initial_velocity):\n",
    "        self.mass = mass\n",
    "        self.spring_constant = spring_constant\n",
    "        self.position = initial_position\n",
    "        self.velocity = initial_velocity\n",
    "\n",
    "    def acceleration(self):\n",
    "        return -self.spring_constant * self.position / self.mass\n",
    "\n",
    "    def update(self, dt):\n",
    "        self.velocity += self.acceleration() * dt\n",
    "        self.position += self.velocity * dt\n",
    "\n",
    "class Simulation:\n",
    "    def __init__(self, oscillator, time_step, total_time):\n",
    "        self.oscillator = oscillator\n",
    "        self.time_step = time_step\n",
    "        self.total_time = total_time\n",
    "        self.time = np.arange(0, total_time, time_step)\n",
    "        self.positions = np.zeros_like(self.time)\n",
    "        self.velocities = np.zeros_like(self.time)\n",
    "        self.accelerations = np.zeros_like(self.time)  # Store acceleration data\n",
    "\n",
    "\n",
    "    def run(self):\n",
    "        for i, t in enumerate(self.time):\n",
    "            self.positions[i] = self.oscillator.position\n",
    "            self.velocities[i] = self.oscillator.velocity\n",
    "            self.accelerations[i] = self.oscillator.acceleration()  # Save acceleration at each time step\n",
    "            self.oscillator.update(self.time_step)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ffa00065",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a harmonic oscillator instance with mass=1, spring_constant=2, initial_position=1, and initial_velocity=0\n",
    "oscillator = HarmonicOscillator(1, 2, 1, 0)\n",
    "\n",
    "# Create a simulation instance with the oscillator, time_step=0.01, and total_time=10\n",
    "simulation = Simulation(oscillator, 0.01, 10)\n",
    "\n",
    "# Run the simulation\n",
    "simulation.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb468482",
   "metadata": {},
   "source": [
    "# Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "60734539",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results using matplotlib\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(simulation.time, simulation.positions, label=\"Position\")\n",
    "plt.plot(simulation.time, simulation.velocities, label=\"Velocity\")\n",
    "plt.plot(simulation.time, simulation.accelerations, label=\"Acceleration\")  # Plot acceleration data\n",
    "\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Value\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "15fdcd38",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c56f3308",
   "metadata": {},
   "source": [
    "# Trial Question 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6540fb51",
   "metadata": {},
   "source": [
    "A container with a volume of 1 m³ holds an ideal gas at an initial pressure of 1.5 x 10^5 Pa and a temperature of 300 K. The gas undergoes an isothermal expansion at constant temperature until its final volume is 3 m³. Calculate the final pressure and the work done by the gas during the expansion. Use the following equation for the isothermal process of an ideal gas:\n",
    "\n",
    "$$PV = nRT$$\n",
    "\n",
    "where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is the temperature.\n",
    "\n",
    "Assume that the gas constant $R$ = 8.314 $J/(mol \\ K)$ and the molar mass of the gas is 28.97 $g/mol$.\n",
    "\n",
    "Provide a Python script to perform the calculations and plot the pressure-volume curve during the expansion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d396b130",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class IdealGas:\n",
    "    def __init__(self, P_initial, V_initial, T, molar_mass):\n",
    "        self.R = 8.314  # Gas constant in J/(mol*K)\n",
    "        self.P_initial = P_initial\n",
    "        self.V_initial = V_initial\n",
    "        self.T = T\n",
    "        self.molar_mass = molar_mass\n",
    "        self.n = (P_initial * V_initial) / (self.R * T)  # Calculate the number of moles (n)\n",
    "\n",
    "    def final_pressure(self, V_final):\n",
    "        return (self.n * self.R * self.T) / V_final\n",
    "\n",
    "    def work_done(self, V_final):\n",
    "        return self.n * self.R * self.T * np.log(V_final / self.V_initial)\n",
    "\n",
    "    def plot_isotherm(self, V_final):\n",
    "        volumes = np.linspace(self.V_initial, V_final, 100)\n",
    "        pressures = self.n * self.R * self.T / volumes\n",
    "\n",
    "        plt.figure()\n",
    "        plt.plot(volumes, pressures, label=\"Isothermal Expansion\")\n",
    "        plt.xlabel(\"Volume (m^3)\")\n",
    "        plt.ylabel(\"Pressure (Pa)\")\n",
    "        plt.title(\"Pressure-Volume Curve for Isothermal Expansion\")\n",
    "        plt.legend()\n",
    "        plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "60ece552",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final pressure: 50000.00000000001 Pa\n",
      "Work done: 164791.8433002165 J\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an IdealGas instance with initial pressure, initial volume, temperature, and molar mass\n",
    "gas = IdealGas(P_initial=1.5e5, V_initial=1, T=300, molar_mass=28.97e-3)\n",
    "\n",
    "V_final = 3  # Final volume in m^3\n",
    "\n",
    "# Calculate the final pressure and work done\n",
    "P_final = gas.final_pressure(V_final)\n",
    "W = gas.work_done(V_final)\n",
    "\n",
    "# Print the results\n",
    "print(f\"Final pressure: {P_final} Pa\")\n",
    "print(f\"Work done: {W} J\")\n",
    "\n",
    "# Plot the isotherm\n",
    "gas.plot_isotherm(V_final)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b950e24",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56c94e49",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b85fc338",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}