chrono.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b319ead2",
   "metadata": {},
   "source": [
    "# TP1 - Mesure d'une durée au chronomètre\n",
    "\n",
    "### Objectif  \n",
    "Nous allons chercher à quantifier l'impact qu'a un expérimentateur sur la mesure d'une durée et déterminer l'incertitude-type liée à celle-ci. "
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "e7164035",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "    <big><b> Consignes </b></big> \n",
    "\n",
    "<ol>\n",
    "\t<li> Rendez-vous sur le site https://chronometre.minuteur-en-ligne.fr/chronometre-temps-intermediaires.</li>\n",
    "\t<li> Cliquez sur \"Démarrer\" puis, toutes les 2 secondes, cliquez sur mémoriser (le but est d'être le plus \"précis\" possible).</li>\n",
    "\t<li> Au bout de 2 minutes cliquez sur arrêter. </li>\n",
    "\t<li> Vérifiez que vous n'avez pas fait de temps intermédiaires supérieurs à 3 secondes ou inférieurs à 1 seconde, sinon recommencez. Le dernier temps peut être supprimé si nécessaire.</li>\n",
    "\t<li> Téléchargez au format .txt votre mesure.</li>\n",
    "    <li> Renommez ce fichier en << chrono_prenom.txt >>.</li>\n",
    "\t<li> Importez ce fichier dans le dossier de travail (cf image ci-dessous).</li>\n",
    "\t<li> Lancez les lignes de code suivantes en suivant les consignes.</li>\n",
    "</ol>\n",
    "</div>\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b278226",
   "metadata": {},
   "source": [
    "**Importation des bibliothèques**\n",
    "\n",
    "Executez les commandes ci-dessous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0a7ddd38",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # bibliothèque \"scientifique\" permettant l'utilisation des fonctions classiques, des tableaux, ...\n",
    "import numpy.random as rd # génère des nombres aléatoires suivant une certaine distribution\n",
    "import pandas as pd # gestion des données (import de tableurs csv) \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c69844a9",
   "metadata": {},
   "source": [
    "**Importation de votre fichier** \n",
    "\n",
    "Renommez votre fichier de mesure en \"chrono_prenom.txt\" puis renommez dans la cellule ci-dessous \"chrono_1.txt\" en \"chrono_prenom.txt\". "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "384f961b",
   "metadata": {},
   "outputs": [],
   "source": [
    "File = pd.read_csv(r\"chrono_1.txt\", delimiter=\"\\t\", header = None) # récupération du fichier txt (3ème colonne temps)\n",
    "#File = pd.read_csv(r'.\\chronometre\\chrono_2s_b.txt', delimiter=\"\\t\", header = None) # récupération du fichier txt (3ème colonne temps)\n",
    "temps = File.to_numpy() # fichier converti en tableau de chaîne de caractères (format \"hh:mm:ss.xxx\")\n",
    "\n",
    "Dt = [] #Liste des intervalles de temps mesurées toutes les 2 secondes    \n",
    "for i in range(np.size(temps,0)-1):\n",
    "    t = temps[i,1] #récupération de la colonne des temps en format \"hh:mm:ss.xxx\"\n",
    "    # conversion en millisecondes : \n",
    "    # des minutes : mm*60*1000\n",
    "    # des secondes : + ss*1000\n",
    "    # des millisecondes : + xxx\n",
    "    Dt.append(float(t[3:5])*60*1000+float(t[6:8])*1000+float(t[9:13]))     "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e21ebc96",
   "metadata": {},
   "source": [
    "Le code que vous avez lancé dans la cellule du dessus permet d'importer votre fichier de mesure"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71ed2774",
   "metadata": {},
   "source": [
    "**Mesure de l'intervalle de temps moyen et écart type de ce processus de mesure**\n",
    "\n",
    "Executez la cellule ci-dessous et notez les valeurs affichées par la commande print(). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "55f7ccc9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vous avez effectué N = 60 mesures d'intervalles de temps\n",
      "La valeur moyenne des durées enregistrées notée Dtm est de 2000.9 milisecondes\n",
      "L'écart-type expérimental des durées enregistrées est de 94.2 milisecondes\n",
      "L'incertitude-type sur une durée Dt censé être de 2 secondes est u(Dt) = 0.094 s\n",
      "Est associée, à la valeur moyenne des durées enregistrées Dtm, une incertite-type : u(Dtm) = 0.012 s\n"
     ]
    }
   ],
   "source": [
    "Dtm = np.mean(Dt) # Moyenne de la série d'observations.\n",
    "ecart_type = np.std(Dt,ddof=1) # Écart-type de la série d'observations. ddof : degrés de liberté => calcul de l'écart type expérimental (et pas \"mathématique\")\n",
    "\n",
    "print(\"Vous avez effectué N = {:.0f} mesures d'intervalles de temps\".format(len(Dt)))\n",
    "print(\"La valeur moyenne des durées enregistrées notée Dtm est de {:.1f} milisecondes\".format(Dtm))\n",
    "print(\"L'écart-type expérimental des durées enregistrées est de {:.1f} milisecondes\".format(ecart_type))\n",
    "print(\"L'incertitude-type sur une durée Dt censé être de 2 secondes est u(Dt) = {:.2} s\".format(ecart_type*1e-3))\n",
    "print(\"\"\"Est associée, à la valeur moyenne des durées enregistrées Dtm, une incertite-type : u(Dtm) = {:.2} s\"\"\".format(ecart_type*1e-3/np.sqrt(len(Dt))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b47d8fa0",
   "metadata": {},
   "source": [
    "**Tracé des différentes mesures**\n",
    "\n",
    "Lancez le code ci-dessous et visualisez : \n",
    " + l'écart-type (double flèche dont la taille correspond à sa valeur, cf cellule précédente) par rapport à la répartition de vos observations (chaque trait correspond à une observation, il y en a N, cf cellule précédente),\n",
    " + comment est placée la moyenne des N observations (trait rouge normalement proche de 2000 ms)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3418c193",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,2)) \n",
    "plt.tick_params(left = False, labelleft = False)\n",
    "plt.plot((Dt,Dt),(0,1), 'blue')\n",
    "plt.plot((Dtm,Dtm),(0,1), 'red', lw=4)\n",
    "plt.annotate('',xy=(Dtm-ecart_type,0.5),xytext=(Dtm,0.5), arrowprops=dict(arrowstyle='<->',lw=2))\n",
    "plt.annotate('',xy=(Dtm,0.5),xytext=(Dtm+ecart_type,0.5), arrowprops=dict(arrowstyle='<->',lw=2))\n",
    "plt.xlabel('Ecart de temps (millisecondes)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f88c8edc",
   "metadata": {},
   "source": [
    "Le trai rouge représente la valeur moyenne ``Dtm`` de votre processus de mesure et chaque trai bleu une mesure unique.\n",
    "Les flèches représentent l'écart type ``ecart_type`` (une estimation de sa valeur) qui correspond à la formule :\n",
    "$$\\sigma = \\sqrt{\\dfrac{\\sum_{n=1}^N(x_i-\\overline{x})^2}{N-1}}$$\n",
    "où $\\sigma$ est ``ecart_type``, $\\overline{x}$ est ``Dtm``, $x_i$ correspond à la i-ème valeur de la liste ``Dt`` et N est la taille de la liste ``Dt``.\n",
    "Une autre représentation est l'histogramme, ce qui permet de mieux visualiser l'ensemble de vos mesures. Pour cela, lancez la cellule ci-dessous :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5eae9251",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#tracé d'un histogramme de la différence des temps (doit être normalement centré sur 0) \n",
    "plt.figure(figsize = (10,6))    \n",
    "num, bins, patches = plt.hist(Dt,range=(np.min(Dt)*0.9,np.max(Dt)*1.1),bins=30,label='Moyenne = {:.{:}} s, Écart type = {:.2} s'.format(np.mean(Dt)*1e-3,len(\"{:.2}\".format(np.std(Dt,ddof=1)*1e-3))-1,np.std(Dt,ddof=1)*1e-3))\n",
    "plt.plot((Dtm,Dtm),(0,max(num)),'red',lw=4)\n",
    "plt.annotate('',xy=(Dtm-ecart_type,max(num)*0.61),xytext=(Dtm,max(num)*0.61), arrowprops=dict(arrowstyle='<->', lw=2))\n",
    "plt.annotate('',xy=(Dtm,max(num)*0.61),xytext=(Dtm+ecart_type,max(num)*0.61), arrowprops=dict(arrowstyle='<->', lw=2))\n",
    "plt.xlabel('Ecart de temps (millisecondes)')\n",
    "plt.ylabel('Nombre des écarts de temps situé dans un intervalle donné')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39ae3333",
   "metadata": {},
   "source": [
    "Vous pouvez changer la taille des intervales des écarts de temps en changeant la valeur du paramètre `bins` dans la fonction `plt.hist()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5c7d1034",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "f898fb61",
   "metadata": {},
   "source": [
    "### Cours \n",
    "#### Propriétés \n",
    "Soit $X$ la notation pour la grandeur à mesurer, $\\overline{x}$ la valeur moyenne de $N$ observations. La i-ème observation est notée $x_i$. L'incertitude-type d'$\\textbf{une seule}$ obseration est notée $u(X)$. Les deux propriétés suivantes sont supposées vrai en physique :\n",
    " + L'incertitude d'$\\textbf{une seule}$ obseration $u(X)$ vaut l'écart type expérimental $\\sigma$ des N observations.\n",
    " + L'incertitude-type associée à la moyenne $u(\\overline{x})$ vérifie $u(\\overline{x}) = \\dfrac{\\sigma}{\\sqrt{N}}$\n",
    " \n",
    "#### Conventions \n",
    "L'écriture d'une valeur $\\overline{x}$ d'une grandeur $X$ mesurée en physique expérimentale se fait comme suit :\n",
    "+ Ne noter que les deux premiers chiffres significatifs du résultat $u(\\overline{x})$.\n",
    "+ Ne noter que les chiffres de \\overline{x} qui ont une puissance de 10 supérieure ou égale à la puissance de 10 du deuxième chiffre significatif de $u(\\overline{x})$.\n",
    "\n",
    "Exemple : Un processus de mesure d'une longueur donne comme valeur moyenne brute : $$\\rm \\overline{\\ell} = 0,123456\\,m;\\, u(\\overline{\\ell}) = 0,0112\\,m.$$ L'écriture correcte du résultat serait : $$\\rm \\overline{\\ell} = 0,123\\,m;\\, u(\\overline{\\ell}) = 0,011\\,m$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1849404c",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    <big><b> Questions </b></big> <br>\n",
    "On note $\\Delta t$ la durée à mesurer et $\\overline{\\Delta t}$ la valeur moyenne des $N$ observations.\n",
    "<ol>\n",
    "\t<li> Quel est la valeur moyenne des durées obtenues par votre processus de mesure ? Que vaut l'incertitude-type d'$\\textbf{une seule}$ observation ? </li>\n",
    "    <li> Notez le résultat de votre mesure en respectant la forme $\\overline{\\Delta t} = ... ; u(\\overline{\\Delta t}) = ... $ où $u(\\overline{\\Delta t})$ représente l'incertitude-type de la mesure de $\\textbf{la moyenne}$ des intervalles enregistrées $\\overline{\\Delta t}$, soit l'écart-type (qui est aussi l'incertitude-type d'$\\textbf{une seule}$ observation $u(\\Delta t)$ divisé par la racine carré du nombre de valeurs enregistrées $$u(\\overline{\\Delta t}) = \\dfrac{u(\\Delta t)}{\\sqrt{N}}$$. </li>\n",
    "</ol>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "032e6c1e",
   "metadata": {},
   "source": [
    "Réponse Q1 : "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99551d9d",
   "metadata": {},
   "source": [
    "Réponse Q2 :"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5276f8b0",
   "metadata": {},
   "source": [
    "### Génerer l'équivalent de 100000 observations de durées\n",
    "\n",
    "Réalisez maintenant 100000 observations de durées de 2 secondes au chronomètre. Stop ! Ne le faite pas, cela vous prendrait plus de 5 heures... N'y-a-t'il pas un autre moyen ?\n",
    "\n",
    "Un moyen utilisé pour générer un grand nombre d'observations en science est de simuler un processus de mesure à partir d'un échantillon d'observations. Les 59 ou 60 observations que vous avez faites vont servir à simuler un ensemble plus grand d'observations que *vous auriez pu* effectuer.\n",
    "\n",
    "La fonction `rd.normal()` ci-dessous permet de générer un ensemble d'observations typiques d'un expérimentateur (appelé *loi de distribution normale*) tel que la valeur moyenne soit ``Dtm`` (variable déjà crée à ce stade), l'écart type ``ecart_type`` (idem) et le nombre d'observations du nombre que vous voulez (ici `100000`). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "88c14626",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Dt_MC = rd.normal(Dtm,ecart_type,100000) \n",
    "Dtm_MC = np.mean(Dt_MC)\n",
    "ecart_type_MC = np.std(Dt_MC,ddof=1)\n",
    "plt.figure(figsize=(12,6))   \n",
    "num, bins, patches = plt.hist(Dt_MC,range=(np.min(Dt)*0.9,np.max(Dt)*1.1),bins=40,label='Moyenne = {:.1f} ms, Std = {:.2} ms'.format(Dtm_MC,ecart_type_MC))\n",
    "plt.plot((Dtm_MC,Dtm_MC),(0,max(num)),'red',lw=4)\n",
    "plt.annotate('',xy=(Dtm_MC-ecart_type_MC,max(num)*0.61),xytext=(Dtm_MC,max(num)*0.61), arrowprops=dict(arrowstyle='<->', lw=2))\n",
    "plt.annotate('',xy=(Dtm_MC,max(num)*0.61),xytext=(Dtm_MC+ecart_type_MC,max(num)*0.61), arrowprops=dict(arrowstyle='<->', lw=2))\n",
    "plt.xlabel('Ecart de temps (millisecondes)')\n",
    "plt.ylabel('Nombre des écarts de temps situé dans un intervalle donné')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0603fd00",
   "metadata": {},
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}