{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c25e271",
   "metadata": {},
   "outputs": [],
   "source": [
    "import importlib\n",
    "from statlib import *\n",
    "\n",
    "g  = 9.806\n",
    "ug = 0.004"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "233e717f",
   "metadata": {},
   "source": [
    "# Calcolo w0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1efad4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# k e m varie configurazioni\n",
    "\n",
    "# k [N/m]\n",
    "k1  = 23.631\n",
    "uk1 = 0.017\n",
    "\n",
    "k2  = 3.2053\n",
    "uk2 = 0.0013\n",
    "\n",
    "# m [g]\n",
    "m_CD   = [63.13, 83.04, 103.02, 122.83, 142.77, 162.44, 182.33]\n",
    "m_rete = [58.96, 78.86,  98.85, 118.66, 138.61, 158.26, 178.16]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81d935ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creazione Data\n",
    "\n",
    "df = pd.DataFrame()\n",
    "df[\"m_CD\"]    = m_CD\n",
    "df[\"um_CD\"]   = 0.01/np.sqrt(12)\n",
    "df[\"m_rete\"]  = m_rete\n",
    "df[\"um_rete\"] = 0.01/np.sqrt(12)\n",
    "df[\"k1\"]      = k1\n",
    "df[\"uk1\"]     = uk1\n",
    "df[\"k2\"]      = k2\n",
    "df[\"uk2\"]     = uk2\n",
    "\n",
    "param_sistema = Data(df)\n",
    "param_sistema.analisi_stat = df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7b2c2af7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo w0 varie cnfigurazioni\n",
    "\n",
    "m_CD, m_rete, k1, k2 = sp.symbols('m_CD, m_rete, k1, k2', positive=True)\n",
    "\n",
    "w0_1_CD   = sp.sqrt(k1/(m_CD/1000))\n",
    "w0_1_rete = sp.sqrt(k1/(m_rete/1000))\n",
    "w0_2_CD   = sp.sqrt(k2/(m_CD/1000))\n",
    "w0_2_rete = sp.sqrt(k2/(m_rete/1000))\n",
    "\n",
    "param_sistema = param_sistema.calc_var(w0_1_CD, \"w0_1_CD\")\n",
    "param_sistema = param_sistema.calc_var(w0_1_rete, \"w0_1_rete\")\n",
    "param_sistema = param_sistema.calc_var(w0_2_CD, \"w0_2_CD\")\n",
    "param_sistema = param_sistema.calc_var(w0_2_rete, \"w0_2_rete\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecf23a81",
   "metadata": {},
   "source": [
    "# Creazione classi dati\n",
    "\n",
    "Selezione picchi delle oscillazioni"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c040f35e",
   "metadata": {},
   "outputs": [],
   "source": [
    "config = [molla1_leggera_rete_inizio, molla1_leggera_rete_fine, molla1_leggera_rete_mid,\n",
    "          molla1_pesante_rete_inizio, molla1_pesante_rete_fine, molla1_pesante_rete_mid,\n",
    "          molla1_leggera_CD_inizio,   molla1_leggera_CD_fine,   molla1_leggera_CD_mid,\n",
    "          molla1_pesante_CD_inizio,   molla1_pesante_CD_fine,   molla1_pesante_CD_mid,\n",
    "          molla2_leggera_rete_inizio, molla2_leggera_rete_fine, molla2_leggera_rete_mid,\n",
    "          molla2_pesante_rete_inizio, molla2_pesante_rete_fine, molla2_pesante_rete_mid,\n",
    "          molla2_leggera_CD_inizio,   molla2_leggera_CD_fine,   molla2_leggera_CD_mid,\n",
    "          molla2_pesante_CD_inizio,   molla2_pesante_CD_fine,   molla2_pesante_CD_mid]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b522bfe",
   "metadata": {},
   "source": [
    "# Rgressione lineare"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30f903b5",
   "metadata": {},
   "source": [
    "## Attrito proporzionale a v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "64e483e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo simbolico x e y\n",
    "\n",
    "# x = n-1\n",
    "n = sp.Symbol('n', positive=True)\n",
    "x = n-1\n",
    "\n",
    "# y = ln(h1/hn)\n",
    "h1, hn = sp.symbols('h1 hn', positive=True)\n",
    "y = sp.ln(h1/hn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b0df03fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo numerico x e y\n",
    "\n",
    "for data in config:\n",
    "    data = data.calc_var(x, \"x\")\n",
    "    data = data.calc_var(y, \"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "497ed583",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Regressione\n",
    "\n",
    "for data in config:\n",
    "    data = data.reg_lin(stampa_param=True, plot_regressione=True, calc_residui=True,\n",
    "                            x_label=\"\", y_label=\"\", r_label=\"\",\n",
    "                            titolo_reg=\"\", titolo_residui=\"\",\n",
    "                            cd_A=4, cd_B=4, scala_barre=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "453d5b53",
   "metadata": {},
   "source": [
    "## Attrito proporzionale a v^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cdb8d336",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo simbolico x e y\n",
    "\n",
    "# x = n-1\n",
    "n = sp.Symbol('n', positive=True)\n",
    "x = n-1\n",
    "\n",
    "# y = 1/hn - 1/h1\n",
    "h1, hn = sp.symbols('h1 hn', positive=True)\n",
    "y = 1/hn - 1/h1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84ad3d64",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calcolo numerico x e y\n",
    "\n",
    "for data in config:\n",
    "    data = data.calc_var(x, \"x\")\n",
    "    data = data.calc_var(y, \"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8fee50b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Regressione\n",
    "\n",
    "for data in config:\n",
    "    data = data.reg_lin(stampa_param=True, plot_regressione=True, calc_residui=True,\n",
    "                            x_label=\"\", y_label=\"\", r_label=\"\",\n",
    "                            titolo_reg=\"\", titolo_residui=\"\",\n",
    "                            cd_A=4, cd_B=4, scala_barre=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc3ce36f",
   "metadata": {},
   "source": [
    "# Stima errore campionamento"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "513736c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_max =\n",
    "w0_max =\n",
    "fc = 50     # [Hz]\n",
    "\n",
    "err_picco_max = A_max * (1 - np.cos(w0_max / (2*fc)))\n",
    "print(f\"errore massimo individuazione picco > {err_picco_max}\")"
   ]
  }
 ],
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