1. The input-output equation characterizing an amplifier that saturates once the input reaches certain values is:
![](data:image/png;base64,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)
Where x(t) is the input and y(t) the output.
a. Plot the relation between the input x(t) and the output y(t). Is this a linear system? For what range of input values is the system linear, if any?
b. Suppose the input is a sinusoid x(t) = 20 cos(2Πt)u(t), carefully plot x(t) and y(t) for t = -2 to 4.
2. The following op-amp circuit is used to measure the changes of temperature in a system. The output voltage is given by:
![](data:image/png;base64,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)
Suppose that the temperature in the system changes cyclically after t = 0, so that:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVsAAAAzCAIAAAC2fTw5AAAgAElEQVR4nO19e1yP9/v/Pac5DhvCHMdHTttSknxyWCI1h4iclk8lIVKIT0KGMLQ5LYeUDXNIJBVmNJRJQ0RTSTpK58O79/k+XL8/Lve1u7dqmfn6/Lb39dhjj7f3+75f9/V6va7reR1fdwzoSU960pNIzNtmQE960tP/EOkRQU960tPvpEcEPelJT7+THhH0pCc9/U56RNCTnvT0O+kRQU9vn3ieZ1mW53n8pyAIHMfRP6WfX75REAT6DAAajUar1eIgWq22thtflQRBEASB53l8In6WPlrKvw6HGo2G47g/8VB8HI5Mz0JiWRa/QWbwS3qKVqvFRZOyqjNCbaRHBD29TeJFQrnneV6lUqE0a7VajUZDSljj7YIg4I0cx7Esq1arNRqNWq3WarUEK6ge9WepNuXB71mWVSqViDXEGzIgCIJSqSwuLpbJZCzLchzHcRwiFClw/deE4zitSDg7fDQ+EadGM0XSarXl5eUKhQJnjc/FcepYQx3SI4Ke3hqhwqC4owSjiJOakXmszdqjbmi1WrlcLhV91E+8ALWr/s6CICHp96TVOKBCoUDAUqlULMviNZcuXZo7d66Pj4+vr+/OnTsrKiqQH5xX/RkglGRZFiESAK5duxYdHY3LRXBA0KDRaARB2LFjR0BAgEKhQIZxHV7JV9Ijgp7eGqHooykjOy91GTiOU6vVtTm9aJNRLVF5UD1I/9HLAFGHX4krnSdyHKdSqRQKRU5OjlwuBwCFQkFAhgxwHJebmxsXFxcQENC2bdtevXrl5OSAqJmvFL9oNBrUcFwcALh48aKHh0dycjLOiyAAmUROACApKWnLli0BAQFlZWX4PYhORz0frUcEPb1NQuEmpwCjbqmbgEJfmz4TFqA/DyJMkC+Nqlh/nxmpRh+B5/nnz58fOnRo165dBQUFAKBWq/GhLMsiMOGVycnJhoaGnTp1ysrKqm20up+OPJNtj4uLmzZtWnx8POUFCALUanVSUhJ+xlUqKiry9vb+6quvcDTE1vqHLXpE0NNbI4wapAqPio2aUB+7ivpPl8lkMvqJHAStVqtSqV6TVcKXsrKywMDA1atXP3/+HEQjjBMhrXv8+HH//v27dOmCPgJOiiKL+hC6BogySqXSwcFhyZIlFCIRDgLA0aNH165di1cSgqSkpNjb20dFRYHoodQ/u6lHBD29NZIG2LGxsREREZgVk3q5KSkpe/bs+eGHH2rUKLysvLx87969ISEh69atW7VqFY4DAHK5HJEFoeE1WaXQQ6vVHjhwYMWKFc+ePQOxFKJWqwngKisrTUxM2rVrl5mZide/qpOiUqlkMpkgCGq1Zt++/ePHj8ehMGdBQwUEBBgbG6enpyMbhKQAcPLkSUNDw0uXLoEYNL1lH4E4+8PSkZTRV3KuXp+IAXquUL2qRD9JE7x4Y/0TRdKhpGWhOq4kNw83kgwC5pnIo6Yp4GVStqGmxdTZiDpWm74nYaJHUBqcriT7g2ZNZ+loCvh0HT7VajUA3Llzx8vLKyQkRKlUEg9JSUlffvllcHCwubk5wzBOTk4nTpzQkRYAKC4u9vX1nTdv3sGDB4OCgmxsbHr27LF8+XIxkNZqNGqe5wEEjmN5nhMEHieBHwAAiwI4JmkOrdXFixfPnj2LfNJGCILg4uLi5uYmk8lws/BLhUKB/x8yZEibNm1u374N1aOGmjRTEARBo1HzPAcAarX62bM8nmc1GjUAPH36dODAAQEB2/FeZIPn+ZiYGD8/v+7du3/44YdLliw5cOAA+kckGBkZGZ07d545cyY+461FDSj0gpgxoixRjdygNGPRiBJL/8eIUCN84peY4yUnVqVSIZ/4DVqDej5IRzGorlYbV9LYGHNIZCF1VAKlBD1DysaR0tb2CLVaHRsbi35vbdwiA7RE+A2m0+hX5BARgVZGuvs4FFYE0ZDK5XKaHbKXmJhoa2t76NAhEF1cAIiPj/fw8PD3909OTk5KSvL39//ggw+aNGny9ddf4ziIHVqtdsGCBZ9//jnqPwAUFxePH2/LMMzBg/t5nhcETqtVcxzLcRqO0/A88qtiWQ3LqmnBpStPHQ0AEBUV1b17961btyqVSrVajTwrFAqO427dutWvX78ffvgBRLNHqIc+QseOHWNiYkDSy4DoiUt65coVF5e5J0+eAOA5TsuyWrVadfz4sUWLFl64ECUIvCBwABAScrB3716xsddARC61Wq1Sqa5fv7558+Y+ffqMHj3a19f38OHD5eXluHQoISUlJePGjTM3N8/Pz4eXjEEd9NcjAtlAkvvapJ8XmzeUSiWu8p9r5HgdbhUKhVqtVigUCoVCLpeXlZXJZDLkByUA9wDjOioyv1LeGIk8YcpL1wYovCTrrlarKX0FAKWlpYWFhYWFhSUlJVBdEGkx8Sm0C0VFRTdv3rxy5Up0dHRkZOSxY8cCAwOXL18+duzYhw8f1vh0dE2pwo/qrRIJ4Ql/wtVAcaciGcEHXoN+DQXGBA3kTXh7e8+YMQNNHI72+PFjFxeX48ePSxk7cuRI27Zte/bsGRsbi+MDQGho6Icffvjjjz8CAKlxcPDBDh3aGRsbP3mSDgBqtUqrVde41FJXq6Cg4PLly0VFRbzYwpCammpjY9OxY8eNGzfu2LHj2LFjmI+gVKijo+OYMWNyc3NBlHwcFhGhffv2Fy9eBNE+0wUFBQWBgYGzZs1q0qTJ4sWLAIDnWQCQy6s++2xUjx7d09JSicF581x69OiWkvIbALDsi+oszjQrK6tv375+fn54Ke64XC6n7Mnq1avbtm178ODBmiWyFnojUYMgSYHI5fLa8jpkDEn9+FepEr0+kU2Li4sbN27c8OHDZ8yYsXHjxszMTKmTTE0pNLu6VbpGIiEmC/mHiIB5eLxMLpcfPXrU3t7excVlxowZw4cPDwoKImmmChwyScYcAGJjY4cMGTJo0CBTU9OPP/7Y0NCwa9eunTt33rp1KwbbOoRQjlU9UmypPiPQS7tuKHGFnCuVSgQOqpzpzA4BApk/efLktGnT0tLSQBJQ3L9/PzAwED1kGqSgoGD48OFt2rTx9/fHobRarZ2dXZcuXTCep1RccXHhlCl2jRs3On06DOCFHhYWFqSmpqSlpWVmZqakPEpKuh8Tc/nrr7dv3rzZw8Nj7NixlpaWp06dQrcfAFJSUnbt2jVs2DAzM7Nz587FxcXdu3cPOSdf78aNG3379t2zZ4909QCgqqrK3Ny8TZs2YWFh0nnhEv38889bt24NDQ0dMGAAIgJSRUW5ubnZsGFD5fIqABAEDkCYM8exS5cPESMQp0hBDhw40K9fv8uXL4OIwrj4JKgRERENGzZcuHChlLc/pL8eEXRcTTILtV2sUqnQm6pbT94En9TNdvr0aYZhjIyMzpw5k5ycXFZWRt6BFKHy8vJSU1PRGEqXvj7PQhmiadYRH6lUqqqqKrK0PM9XVFQ4OTmZm5tHREQkJSXduHHDxcWlWbNmX331FSbPqMJEK0/ocOHChcGDB4eHh9+9ezchIeHmzZsJCQlJSUlyubw2BhDNa8zGodbhQ/GbyspKLMXRvfhochnKyspu3LgRHx9/7949HBMdHwDIzc0dOnTo3LlzaeKII1qttqqqCuMyNCo8z8tkMnt7+3bt2p04cQKvLy8vHzlyZN++fdFKgwQ+5s+f17Jl8+XLvZRKBcexly5dHD/+86FDhwwdajZo0KdjxoweN8565MgRQ4aYmJiYdO/evWfPnnv37lUqleTYy2SynJwcJycnY2Pjp0+f4vgUjhH/AwcOtLe3p64HXFKlUmlnZ9e5c+fAwEBCbZ7nESvLysqUSmVcXFyLFi28vZejgABAXl5ut25dzcxMKyrKAUAQeJVKOX36tE6dDH777SFAtbybIAi+vr7du3dPSEjQERu6JjY2tlGjRq6urnWJ5kv0RnwEFAuNRkNWqEZEQNYrKioqKipA4sL9nxFltiIjI5s0aTJlypSMjAwQERelUxCEsrKymJiYM2fOWFtbDxw48PHjx1A9HfXywOJ/IPkA6enpe/bsuXnzJgAIQo1JJgBJWAGiJxwcHNyyZcsjR47QNRkZGaampg0bNjx69CiImoA3YuoRRJtw5cqVsWPHYpShQ9K6nXRNKDUAAHfu3Dlx4sT58+eTk5MxUsXmGQDIzMy8dOlSdHT08ePHT506dfHixcrKSpC0ygFAQkLCggULrK2tp06d2rdvXx8fn8rKSmQSAK5evdqiRYvVq1eDaBsoNMNJkbPN83x5ebmlpWWPHj1SUlKQ1czMzGHDhllaWhYVFQEAwjcO/s03ASYmg+zsJslksufP893dFyxcOD8q6tzp02HDhw8LDj6YnJycmpq6f/9eQ0PDkJCQvLw8kPi2hPWOjo6mpqa441KjhWJTUlJiYWHx6aefFhYW0t4BgEKhmDlzZpcuXVatWkVeG95OqHH16lUDA4NNm/wBgOPQm7vevn37xYsXabUvsFihkE+cOL5nzx5paSkgqYCiMXN2djYwMMCeJWmuh/bu+vXrjRo1cnNzq0VKa6Y3ggjSLEtiYuKdO3dqyyMAgEwmO378eHR0NLxK/uOv4hOfGB4e3rRpU2NjY2KD8rqVlZXHjh374osvJk6c2Llz506dOlHfWC2jCgC8+B99BgC4cuXykCGDAwPRyeRZVoO5bt37BYECAUwE2NjYuLq6ohYRz7t27WIYZsGCBWVlZVqtVqFQoCuO6EDuz6VLl8aOHZudnY2DS5MOtcE0Try4uHjXrl1OTk6TJk2ytrbu27fvggULELsBID8/38XFxdXVFV2PBQsWmJubOzs7o7pSoNuvXz8TE5MnT54UFhYePHiwa9euCGGoFZGRkS1atPjmm29AEouhLcVAkrwJ5MfIyGjOnDkUcaSlpZmYmAwdOhSjBoIqQRAuXjxvZmZqbm5WUPBcq9U+f56PPz1/nu/i8p/79xNxzK+/DjA0NLxz5w7yjCNTHjcjI8PCwsLFxQULgdI0EG5NSUnJsGHD+vTpg04EXaNQKKZPn96xY0dvb29WbFigoBhXft++fQYGBidOHAcAQeBZVrtsmWfv3h/FxFwBEDgO0ZCfMmVy7969MjLSQfQRKDc3bdq0Tp06paamgsSKSM3JjRs3Gjdu7OTkRDtbi8RWo3ohQk5OzunTpx8+fKjVaktKSs6fPx8UFLRnz55z585VVVXR81DUpCmWR48erV27NioqitIE0riArrx27dq8efN++ukneqIUTaUjgyQqw9vJTdKZMGUBdO6iAaW/nj9/vmvXrn379qVsFrkAubm5MTExBQUFFRUVn3/+ebt27XAPave6X2ABut6CwAkCh6CQmvpo/PjP9+zZBQCCwPK87vE1mggvOTAXEhLSuHFjzGkLYhofAK5evdq/f/+ePXtev3795dXAiBcAbt26RdVsKdVdKyksLPTy8po4ceJPP/2kVCqzs7OXLFni4uJSXFwMAAUFBdbW1lOmTCHXQ6VSRUVFNW7c2NLSEhv1AODbb799//33PT09adiZM2euW7eOdmHnzp0GBgYnT56kb2jxlUolKxLKw7fffmtsbEz1PAC4c+eOkZGRhYUFmmhpE87Fi+eNjY3GjBldVPR7RMPz7LZtXzk6zs7OzgKArKynQ4YMdnBwQF8JIx1e0hkVHh7epk2bwMBAyQg8Zljwc2lpqYWFxcCBA6lbmRfPX3p4eHTs2HHlypWU6KU8C2LukiVLzMzMnjxJRxdSLq8aMsTU0PBfjx9jykCDwd/kyXZdu3ahPAI53VVVVXZ2dv3796eIied57OYgYLp582bjxo2dnZ3pAumO15azqxciZGRkHD582M/Pz8nJycHBYc2aNd988423t7elpeXUqVN37NiBK0KZD9zFX375ZebMmVFRUYSOUj8Z0Y6U4dGjR+7u7pQ0xk0iIJDeTp+lH0ijUIYIejjJiRd6NJlZohs3bgwcOLBnz56hoaE6c5cu4pgxY9q3b48NIS/nzOgOnmd5nhMr4ZxKpVAq5QCQn583e/bM7du24mUcx0pZklY0ERHwp82bNzMMQ4wRIpSUlDg5OfXp0+fXX38lVsmtRfkAgLt3744dO/bChQvr1q1zc3Pz8vJas2YNujm1hWno9BoZGWF5kq6pqKjAJKuPj8+7776rUwuQy+U+Pj4Mw5DOHzp0qEOHDuPGjUOvGwAuX758/fp1FES5XO7h4dGlS5dTp06BpPEBSaPRYFoBF+T58+dDhw7FkQWxYTk7O3v48OGmpqbIJ+V9BIH/5Ze4Tz4ZOGzY0LKyUgAQBE4QBJVKOXeu065dO5GZq1d/btasqZeXF/HPVj8FEBIS0qxZs2PHjoHYZSRN2QCATCYbN25cv379kAFaT7VavW7dunbt2rm7uxMiYDiDqYri4mJra2s7u8lKJWq4EBi4p2NHg759+2JZAdOKLKtdvXpV794fJSTcAgClUoElOQBQKpWTJk0aOnQooqFCoSgrK6NaGLL3448/tm/ffu3ataQCAJCfn3/x4kWqo79sFV4havDz88P0GwbbABATEzNq1CiGYTw9PTEbR7VcuVw+ZcqUL774AiWbeq1wgcLCwsLCwnALCfY2b95sZGT0+PFjqaRSSEw+GwCwLIudISQfFKRxkrI8Vm6lpkPHU6DPd+/eNTExad68eXBwcG3T5zjOxsamefPmv/32W90LxXFY62Y5Ts3zWq1WqVbLASAvL9tu8gT/TRvwKgCeZbVoDAnLiHnibdOmTQ0aNDh79iyxjfut0WgWLFjQoUOHn3/+GSRdSayk4x0Abt++PXjw4O3bt+/YsWPTpk2DBg1iGMba2jo0NFTaDkQkCEJQUFDr1q13794NoutBDjkAJCYmduzYceLEiZg1EAQBE2YAcOnSpVatWpmbm6Mlf/r0aY8ePZo0aWJhYbF37168HkQwLS0tnTVrVo8ePUJDQymQ4cSuDalkozfh7OyM+QIybjKZzNraWqqQLMtyHC8I/M8/X+nd+yMHh6lyuQwAtFo1y2rlcvmMGQ6hoS9ckujo6PbtPwgJCaF7UWBI9tauXcswDAKWNMjCywCgoqLCxsZm8ODBqJaEFCqVavny5Z07d/bw8MB1o1os/vPBgwdt27adM+c/OGBo6Mnly5daW4+xsPh3RUX58+f56emp6DuEhp7o0uXDoKADIPZlkz2wsLCwsbGRyWSpqalbtmxJSkqixUE29u3bZ2JicuvWLVIfmUy2aNGi1q1bb9y4kdZWRwBeARFwgVBnaHUOHTr03nvvdejQ4dy5cyBxtk+ePDl9+nRKwknVMioqql+/fmfOnMGVoupuZmbmhAkTfHx8BEmpBkTMJpvPSvq0SX/QPcFrCM4xMpSmAKWfyQcBgIcPHw4fPrxt27bS7J0OCYIwceLEpk2bUi6nNq+b4zUsqxRAy7JKllXxgobllLygVank7ovd/Dd9CQACaAF4jnsxfZ7nsXRPnNPga9asadiwISY4pGAPAMuWLWvRogU6VvQTTlkul1P2Kzo6Gv0aAEhLS5s7dy7DMN26dUtMTHyZ+ZKSEmNj44EDB5aWloKkb58KRpcvX2YYZsmSJbSMGo0GwSUuLm7QoEG9evU6ffo0AGg0mvDwcFNT00aNGnXq1MnKymrv3r3kW1VUVLi5uWFmgaIhHZeQZMzIyOjKlSu0a2QnbWxsDA0NEREo4wAABw8eaNu27c6d3wgCh21HAHxZWYmPz8qYmCsAoNGovb2XjR5tiQ08JIpIONOVK1d+8sknZABwgwRJC2lRUdGnn35qamqK0ROJk0ajWbFiRbdu3RYtWkTdAazYnAYAN27caNWq1bJly+Ry+Y0bsStWLL99O2HevLlWVpYXLkQHBGzLyclCRHjyJH3gwAFjx1phSZLW5MGDBwMGDDAzM/vll1+2b99+9OhR7NGiaktRUdG4ceMmTZrEi8dAAaCsrGzChAmtWrXasGFDbQL8CoiwatUqhmFQk8nAhoaGdunSpUmTJthzhhynpaVZWVlt27YN1xG5wRgsNjbWxMRk3LhxKSkpT548qaqqEsT+FgD4/vvv+/fvj4ExL+l6hOqZJzSDmLV+OSiojcidln6DG3b//n0zM7P27duji1gj8TxvY2PTrFkzFJE6Mos8r1FrqjheQ1UG+rBh49pNm9bXNj7pg3TWS5cufeeddxBwdTrkV65c2bZt26tXr0pnhDdKe+zwJ9KxkpKS8ePHN23a1NfX92U3obCwsEePHn379i0vL4fqSWIUtZiYmIYNG3p7e+P1VCMEgISEhD59+pibmyckJBCTjx8//u6774yMjBiGad26dXBwMB3UW79+fYcOHQ4fPgwS0EFQI/f41q1bFhYW6LDQLMhLmjx58nvvvffdd9/pIKm//4YPPng/Lg4FicU8Tlxc7MGDB7KyMgEgM/PpJ58MnD17Fq5VZWUl2hs6N8lx3Pz588eMGYPanpCQ8ODBA5QWWsni4uJPPvnE1taWGigJEZYuXdqhQwdXV1dCBGotBYDIyMgGDRpYWVl9+eW6RYsWxMffLCkpHjTIqEWL5nPnOt25cxsAOE6DbYvh4Wc++WQgJVDo0fb29gYGBhQD0q+8mNEfMGDAgQMH8CdyP9PS0mJjY8vLy3VcUaL6IoIgCJ6engzDYIoLRKN08uTJ9u3bt2rVilJfAHD8+PF27dphnCltRoiPjzc3N2/ZsuXw4cNtbW1nzJiBMTAn9snfv39/0KBBvr6+FH2BpOhCeYTamOR5HvsOKysrKysrKyoqiouLs7Ky0tPTKysrSccIRNAyA0BycvKIESPatGmDuFYjsSw7duzYhg0b3rp1C+dVIwZxnEajUVDpUaVWVMrKZbIKuVxWVVX5Xx/vVb4rCgufp6U9Srx3JyHhVmxs7NWrVx88eIBSxYpN04Q4a9eubdSoEUYNOlu4aNGi5s2bIyJIJ0WhuBRAyWMCgE2bNnXu3HnEiBEvNzIXFxcbGhr+61//QhedVon28dq1aw0aNJg7dy4OhTUOxIXExMSePXtOnDixrKwMC+807OPHj319fVu2bGloaEgl9KNHj7733ntbtmwBUWcESX8UABQUFLi6uu7evRshQCt5kwLO8ciRI61bt/7ss8/Qo8EIVKvVWFmNtrGxLi3Fzs4XAOTkNGfHjq+x1JeYeLdTpw4eHotlMpmvry/uu9T+p6enm5iYGBkZ3bt3LzEx0d3d/d69e1D91FBcXFyfPn0wrKBmCpSNNWvWNGvWbOrUqQQi1KYBAHfv3h0xYoSJiUlAwPbU1FQAobS0ePbsmd7eyx49epFH4HkWOS8vLxsxwmLyZDsQbRgykJWV9euvvz558gREDZKegzpy5IiHhwfVZbWSQ1CkLNJgkKi+iFBUVDR9+vSWLVviEUuSy5CQEIxLs7KyBPHlDcuWLTMxMaG6MSeSQqEICgp69913fXx8MjIynjx5gs0n0gSSvb39qFGjMDcujRQEsVbMsmxpaempU6fCwsLCw8PDw8PPnTsXERFx+PDh7du3r1q1avny5WvWrPHz81u9erWPj8+cOXNmzZpFHbtkfokrfK6Li0uTJk3IFr1MHMdNnjy5adOm2CVWGzDxvJbn1U+fph0M3rtt+6ZNW770WbV8ufeS9RvWbNvuP9R88MRJn/tvWjfnPzMn2dlYfjbS1sbG2tp6zZo1z549o0QMMQkAW7ZsadiwIfoIOoDo7u7+/vvvx8fH045wYpchheUcx1EKncQlJCSkU6dOZmZmVEgnysvL6969e5s2bcLDw0GiJCRM8fHxBgYGVOPAX7EHOTExsW3btlgAVygUISEhJAMAUFpa6uDg8O6776L/DwDXr19v3LjxypUraWrkjwBAdna2i4vL/Pnza9sOEOt8DMNINy4gYHu/fn2uX7+K/3z8OOXIke+XL1/aq1fPqKhI/DIz8+lnn43q06fP4sWLFy9ejGsoXa7s7Ozp06d/+OGHGzduDAoK+vXXX6UuKg7i6elpafki7qiqqmLFFlhBEPbt2/fBBx/MnDkTTQ7FuQT3JSUl2dnZ+PIVAEGtVpaVlWg0KnhxIosVBE6plGNvwuXLP02YMAGRlK9esAMxrYaoTT7InDlzsCaK3jQdHSIGiFWdha0vIqSkpNjZ2X388cexsbH0ZWFh4ejRoz/66COpkuTm5g4YMMDGxoaal6XuXGho6DvvvLN//37aV52Ep6enZ+PGjVFoWLHXhZNUGQAgJyfHxcXF1tbWzs7Ozs7OwcHB0dHR1dXV3d3dy8vL19fXz89vzZo1GzZs2LNnz759+77//vucnBwCLKpak80sLi728PBgGIbeM4EkiIT/XLRoUbt27S5cuKATz79EQlzcVdd5znPmzFq5cukq3xXeK7z81q3esWP76NEjXVzmRJw7cy4yPObnn+LirmdlZeXm5hYVFVFmUeehO3fuZBhm5cqVGGFpJeeX5s+f37RpU9wRKTO035RzFcQEIS/2Mrz33nsLFy58ucG8srJy1qxZDMM4ODhQ8kmaBpLJZJiJwLWSBvzffvttgwYNMFenVCqdnZ1dXV2l4b2Li0vjxo1/+eUX/GdmZuaQIUOmTZsmdQEEQSgvLw8KCurXrx/DMP379/f39w8JCQkKCgoJCdm3b9+ePXvItQSA/Pz8WbNmmZiY+Pn5HThw4NixYwsXLjh0KBgAsN3j4cMHs2fPsrIaffjw9xzH4q4CQFpamqPjF0uWLKECHlf9vFZeXl54ePjNmzexCwN9JdwCAEhISDA2NkZBJdwkifrxxx+7detmb28vbX4nGa4ecgrkDgAAFq0pRcjzLPqbeDwUTzdD9VZ3ofrpm8uXL69cufLGjRvEGIEI/VOnGVdK9UWE5OTkUaNGTZ48mVpWY2JiNmzY4OrqShiB0pacnNy8efNRo0ahG0x2Hrfh4MGDrVu31in74xrhBUuXLmUYBhNpOl1rIOlTUKlUcpEUCn9lxcEAAAxXSURBVAWGzSj9nIRIT3ix84SVnNWTIsKiRYsYhsHcB90iDekBYPHixS1atDhx4oQ0rn6JBIAXO6RWq1lWy3G/n4/y99+watV/67PgvFiATE9PHzVqVKtWrbDZkSZVWVk5adKkUaNGYfeRDjxRRlBnTPxga2uL0Fbjox8+fDh48OCWLVt+/fXXOl4lHV4ePXq0lZUVWgJ8UGBg4JgxYzZv3lxSUoLPjY6O7t27t5OTU1hYWEJCgq+v77hx47766qu8vDza0B9//HHw4MGUJUG2k5OTZ8+ePWPGDHd393nz5s2ePdvJyWnu3Lmurq5OTk4zZswICwvDYh5B86lTpxwdHR0cHPbu3SvtkQEAnhfw3GqNi1ybYrxM4mgv3shgb2/v6OhI72ghUcHLbt682bVrV0tLSzI/Lw9Vb3px8U8//bRixQrKGoBY76cgEfXi2LFj2DLz56i+iHDlypURI0YMHz7c1dXVx8dn/vz5rVu3HjlyJDVpkr/34MGDFi1aTJw4kbIAhP2CIGzbtq1nz54oSdTEzopnaQAAbfX58+dBsgfSutQrruYLIoOJ20YdgVrx9C6W/clHoIBc6sqi/7Jjxw6y56/Kxvr1X6KTXAeRqaGk7Pr16xmG2bp1K10AANHR0R07dty3bx+IsKtSqc6ePbtly5Z79+7hKlVUVCQkJJSWlkqRNzAw8OOPP965c2cd/N+7d2/ChAlNmzadM2fO7t27z5079+23365atYpGzs/PX7Zsmamp6X/+8x8vLy8vLy9PT0/sRwRRUrVabXBw8IIFC3bu3BkSErJw4UIsi6B+YmWe4zhHR8fRo0djbRKD4aKiIioBgOjWcWJpiSp5aOjIaeIl7YZvgnixBaiysnL79u1Lly4l50IQ09508aNHj/r374+IIIgJ7NenR48e3b59m5LHWvE99JRYfaVXvNZI9UWEEydO9OrVa+rUqRs3bty5c+eyZcsYhhk8eHBxcTHqFRn5pKSkZs2aUdmDlzQXyeXyJUuWfPrpp3fv3gVxp+lGvN7Ly4thmMjISKjuaPHiyxTILBA0kLbjuzExpyil8vJymUyGh3lZlsX6OYXcOE5wcDDDMJjlkhKhBgAEBAS8//7727Ztk+Yg6kOCGP+vXbt2xYoV9GWNF2MoS2exAeDevXuDBg3q1KlTXFwcntq+c+eOsbHx559/npubK4gdCikpKb1792YYhk7I3r59e+TIkdbW1osXL8YOJUdHx9WrV58/f/4PgbWwsPDAgQPOzs5Tpkzx9PTcuXPnvn37cnJyMB+E/J89e3bjxo3r168PDAzEdkZaLh0HrbCwUOpYseJBaY7jkpKSpk6dSnVfOv1Nu08pYRqNl7xYlRPfXESc15F7fh2iesG1a9f279+PrhknaYEDsaCmVCp37drVsmXLkSNHosPyl+AUzYsTXwPLij0+WvFF7JjOeJ2n1BcRoqOjmzdvTjWnqqoqS0vLbt26URCLXAJASkpK69atraysqNmTBikvL58xY8a///1vTJCSz0b3AoC3tzfDMJhap1wOVM/lVlVVnT17FoPGw4cP7927d9u2bX5+fv/9738XL17s4OBgb28/ZcqUySLZ2tp6enoWFhYiHOCw1C6Ce/nDDz8wDLNx40Zafc1Lr6ZDWPTz83tVP4UQYd26dXX7CGRtKIeC6nf//n0rKytjY2M8TWBra+vj40NCiXyWl5dv2LDB2dk5MTERx8nNzT1z5sz+/fsPHToUFha2f//+4OBgKiLUxoPU/VEqlRkZGSkpKWR5MEFd4+1kwAUxZSNtrIDqR8LJjwCAR48eubm5nT17lo51U6hI7ifeS9snSPpTpWlUqan4C4l2kOO4rKwszCxw1XtwcXHS09OvXbsWGRl54sSJK1euUB/Xa3JF7qpUenHutBp0wes8qL6IcPTo0QYNGkhfz7B7927sVqSYGRUsPz/f1NSUWhulwdWzZ88sLCxsbW2x1o3zpHdy4IpjHgEDS+k7OeRyOUoDABQWFvr4+EycONHV1dXNzc3d3X3FihWbNm3avXv3kSNHIiMjIyMjsQARERFx7ty5M2fOxMTEIOiwkgZHlCSMMBERCPLIygmCoFQqCwsLU1NTFy5cyDCMmZnZb7/9lp2dLa2u1U0kT1u2bPnDqIGiFUGSMQKAnJycqKioCxcuXLhw4fr166zYckveIzq05H5ra//LJdT99rKYkqbhKhEQcGLnIid5AzrP8/SWN2qMpXwN7Z001qX4kRWPaWrF14r7+/vfvXuX8tDStChF6ZSDpKoeskQGg6upxv76JLXDIGIfeQeEdDzPFxcXZ2dnU36BVuM1FZWr3pVHmREUABB7/2vc01ei+iLCoUOHGIYJCAgAMV/14MGD3r17d+vWjQoN+L1arV6xYkXHjh2pl4nWMS0trVu3bo6Ojvh9ampqaWmpWvKqMgBYuHAhVdTo4AMFjbzYAZKbm5uRkZGdnZ2dnY25enrXRR1EsshL/gAWbtXp06ebNGmycOFCnbwUx3EVFRVhYWFubm4WFhb29vbOzs5bt27dvn071dXrT1u3bl20aFHd4QYpAwBgpMNLKl5EFI6x4uuMqJSAOFJVVYUaglBI86WIqbaWCtoy7JYnE4QeKY6A8Rc60uTokdmnv8tEQky1N3J/EBGoMgoABQUFpaWlUv2nDBRb/QWTFLXxYtpcEDtW3lAqQeqSaMWXgxFaUVRLHjFdjH36f4mPQKDMSsqcrPh2HGl4/joP0kUEYl1nDjt27KCqL2UBw8LCpGUq8vyPHz/+zjvvUExOxurXX39lGAZf4XD27NklS5ZQ/x8h7vTp00eOHEmvvkY2cP5o9+CPUrV1rD5fPbdMphgAIiIiWrZs6ejoSE3y5LZotdqioqL09PSsrKzKysrS0tK8vLy8vDzCjvrT2bNnqZO3Nial4kVLJ4jHYFECpL06NC8KsLmX2ropyiV6OSaSrhIvOfkrVVFeTF/x4slcTiwME7xKbQDhFCepH5Nwk/ugk5Yj1SKzTLOjqUmZpFmTwLzqvtSHeLFxRur1SHnWVn/7JoorsfeaRLtAPhr5JoQFUOeLjutJuoggHZo8xvz8fHt7e4ZhsI9AEEuyOTk5JiYm2OWem5vLizn89PR0Y2NjOlVGJu7BgwcGBgb9+vU7ffp0QEDA1atXKWLEh6ampo4ePXrz5s3SG0lp67PZryQNnKQbIjo6ukWLFo6OjhRmS6n+Y9ZN/KuUu3RIqB6yvib96UFe9cY3pJ9vhf60Kfr/iGrwEXjJ39WprKy8ePHinDlzmjVrxjDMiBEjjh8/jp3eOPn4+Ph58+ZNmzbt/Pnz+EpFVP4zZ85YWlpiwy8vHluQy+VhYWGurq4HDhzAVALmimgdd+/ePXXqVDxbDZKekDc0eVZSy4yOjjYwMHBycioqKhLEJD9byx/81ZOe/q6kiwholik2q6ioiIiI8PPz8/f337Rpk4+Pz3fffVdcXKzTJq1Wq589e1ZaWkpOpkwmGz9+/KxZs/CCl/NYgtinQK8eiY+Pt7Ozw2NzfPVegDcKChixR0REdO/e3dXVNS8vj17dQ/Hq3wD79aSn+lANiMCLlf/aMjSYuKKwUPo93oUxxd27d93c3DC/CNVLidIwGJ/46NEjDw+Pbdu2Ue6QjPPreNp1E6ESAJw8ebJVq1aGhobh4eGPHz9+/vw5K/lzY2/i6XrS0/8g1YAIlEcgdeV5HjuFQcx5Ytcw5aiUSqVObhlt7JMnT9zd3c+dO0eqxYudgqiHeFl2dvaqVauOHDmCr07CeIxSMtIU7l9LlK3lef63337bv39/WFhYWlras2fP8O98v9FMlZ709D9INecRSM+xjMRVPzdeXl6OEAASpcIXy0irzVrxgHNAQAC9HxK1C91yylAWFxffvHlT2t0lSF4Q9kYdBIK8Gi/Qw4Ge/mlUAyLolHykxSHqtaDggvSfknCCWManYmFJSQm+zRaq92BT0oG0Tjos/fomysv0OEFSlgNJm53UQfjb48I/YY56qifV0KFUh3BIf9JJE9Z4Zd1y9oe1nDp+/cuJAKvGCf5dSRDbjalI9E+YtZ7qIP1fi//nEjliGo2G/oYS+2dPl+rp70F6RPjnEjlE1AgIf5c2Gz39adIjgp5+P9b1thnR09snPSL8o4mqOax4xFiPC/9w0iOCnvS1Bj39TnpE+KcTYYEeFPQEekTQk570JCU9IuhJT3r6nf4f2+qLh6aEgrYAAAAASUVORK5CYII=)
Let the input be Vi(t) = 1 volt.
a. If the switch closes at t0 = 0 msec., plot the output voltage V01(t) for 0≤t≤0.2 sec. in time-intervals of 0.01 sec.
b. If the switch closes at t0 = 50 msec., plot the output voltage V01(t) for 0≤t≤0.2 sec. in time-intervals of 0.01 sec.
3. A zener diode is such that the output corresponding to an input Vs(t) = cos(Πt) is a "clipped" sinusoid
![](data:image/png;base64,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)
Use MATLAB to generate the input and output signals and plot them in the same plot for 0≤t≤4 at time intervals of 0.001.
a. Is this system linear? Compare the output obtained from Vs(t) with that obtained from 0.3 Vs(t).