Pendel.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Erdbeschleunigung mittels mathematischen Pendel\n",
    "\n",
    "Michael Wollensack METAS 09.09.2022"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from metas_unclib import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eingangsgössen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_gemessen = ufloat(1.2453, 0.0036 / np.sqrt(10), desc='Zeit Gemessen / s')\n",
    "dtau_reaktion = ufloat(0.0, 0.1 / np.sqrt(3) / 20, desc='Zeit Operator Reaktion / s')\n",
    "dtau_ablesung = ufloat(0.0, 0.005 / np.sqrt(3) / 20, desc='Zeit Operator Ablesung Uhr / s')\n",
    "\n",
    "L_gemessen = ufloat(0.33316, 0.00029 / np.sqrt(3), desc='Länge Gemessen / m')\n",
    "dL_meter = ufloat(0.0, 0.0005 / np.sqrt(3), desc='Länge Meter / m')\n",
    "dL_ablesung = ufloat(0.0, 0.0005 / np.sqrt(6), desc='Länge Ablesen / m')\n",
    "\n",
    "D_gemessen = ufloat(0.1005, 0.000071 / np.sqrt(2), desc='Durchmesser Gemessen / m')\n",
    "dD_meter = ufloat(0.0, 0.001 / np.sqrt(3), desc='Durchmesser Meter / m')\n",
    "dD_ablesung = ufloat(0.0, 0.0005 / np.sqrt(6), desc='Durchmesser Ablesen / m')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Messmodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau = tau_gemessen + dtau_ablesung + dtau_reaktion\n",
    "L = L_gemessen + dL_meter + dL_ablesung\n",
    "D = D_gemessen + dD_meter + dD_ablesung\n",
    "\n",
    "g = 4 * np.pi**2 / tau**2 * (L + D / 2 + (D **2 / (5 * (2 * L + D))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ausgangsgrösse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.827632967475104 ± 0.05075049836807857\n"
     ]
    }
   ],
   "source": [
    "print(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unsicherheitsbudget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_budget(output, inputs):\n",
    "    jacobi = get_jacobi2(output, inputs)\n",
    "    unccomponent = get_unc_component(output, inputs) \n",
    "    print(\"Eingangsgrösse                    Wert            Standard         Sensitivität   Unsicherheits   Index     \")\n",
    "    print(\"                                                  Unsicherheit     Koeffizient    Beitrag                   \")\n",
    "    print(\"------------------------------------------------------------------------------------------------------------\")\n",
    "    for i in range(len(inputs)):\n",
    "        print('%(inputname)-32s %(inputval)15.6f %(inputstd)15.6f %(jacobi)15.6f %(unccomponent)15.6f %(index)10.3f%%' % {\n",
    "            'inputname' : inputs[i].net_object.Dependencies[0].Input.Description,\n",
    "            'inputval' : get_value(inputs[i]),\n",
    "            'inputstd' : get_stdunc(inputs[i]),\n",
    "            'jacobi' : jacobi[0][i],\n",
    "            'unccomponent' : np.abs(unccomponent[0][i]),\n",
    "            'index' : 100.0 * unccomponent[0][i]**2 / get_stdunc(output)**2\n",
    "            })\n",
    "    print(\"------------------------------------------------------------------------------------------------------------\")\n",
    "    print()\n",
    "    print('%(outputname)-32s %(outputval)15.6f %(info)34s %(outputstd)12.6f' % {\n",
    "            'outputname' : \"Ausgangsgrösse\",\n",
    "            'info' : \"Kombinierte Standardunsicherheit\",\n",
    "            'outputval' : get_value(output),\n",
    "            'outputstd' : get_stdunc(output)\n",
    "            })\n",
    "    print('%(dummy)-48s %(info)34s %(outputstd2)12.6f' % {\n",
    "            'dummy' : \"\",\n",
    "            'info' : \"Erweiterte Messunsicherheit\",\n",
    "            'outputstd2' : get_stdunc(output) * 2\n",
    "            })"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eingangsgrösse                    Wert            Standard         Sensitivität   Unsicherheits   Index     \n",
      "                                                  Unsicherheit     Koeffizient    Beitrag                   \n",
      "------------------------------------------------------------------------------------------------------------\n",
      "Zeit Gemessen / s                       1.245300        0.001138      -15.783559        0.017968     12.535%\n",
      "Zeit Operator Reaktion / s              0.000000        0.002887      -15.783559        0.045563     80.602%\n",
      "Zeit Operator Ablesung Uhr / s          0.000000        0.000144      -15.783559        0.002278      0.202%\n",
      "Länge Gemessen / m                      0.333160        0.000167       25.282355        0.004233      0.696%\n",
      "Länge Meter / m                         0.000000        0.000289       25.282355        0.007298      2.068%\n",
      "Länge Ablesen / m                       0.000000        0.000204       25.282355        0.005161      1.034%\n",
      "Durchmesser Gemessen / m                0.100500        0.000050       13.975757        0.000702      0.019%\n",
      "Durchmesser Meter / m                   0.000000        0.000577       13.975757        0.008069      2.528%\n",
      "Durchmesser Ablesen / m                 0.000000        0.000204       13.975757        0.002853      0.316%\n",
      "------------------------------------------------------------------------------------------------------------\n",
      "\n",
      "Ausgangsgrösse                          9.827633   Kombinierte Standardunsicherheit     0.050750\n",
      "                                                        Erweiterte Messunsicherheit     0.101501\n"
     ]
    }
   ],
   "source": [
    "inputs = [tau_gemessen, dtau_reaktion, dtau_ablesung, L_gemessen, dL_meter, dL_ablesung, D_gemessen, dD_meter, dD_ablesung]\n",
    "print_budget(g, inputs)"
   ]
  }
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