{
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   },
   "outputs": [
   ],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Question\n",
    "\n",
    "The goal of our predictive question is to determine the farthest horizontal distance that a child of given mass (40 kg) can jump off of a swinging swingset. This is an interesting question to explore, as almost anybody who chooses to jump off of a swinging swingset will want to travel the maximum distance possible for maximum fun. So, we will be able to explore that maximum distance for a 40kg child."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Model\n",
    "\n",
    "We will implement our model by creating a system to execute a sweep of different angles that will give us varying displacements in the x direction to ultimately find the optimal (maximum) distance.\n",
    "\n",
    "We are neglecting any drag force and frictional force on the seat. In the real world, these forces (particularly air resistance) will play a role when calculating the velocity of the swing, for example, but for the sake of simplicity, we will exclude these external forces. This may result in less accurate results, but we estimate the results to be in the range of reasonable values.\n",
    "\n",
    "Our parameters include the acceleration due to gravity (9.8 m/s^2), mass of child (40 kg), mass of swing (5 kg, chain mass negligible), length of chain (2.5 m), initial angle (225 degrees), initial angular velocity (0 radians/s, no initial push), and time duration of the pendulum simulation (15 s)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# Here are the units we'll need:\n",
    "\n",
    "s = UNITS.second\n",
    "N = UNITS.newton\n",
    "kg = UNITS.kilogram\n",
    "m = UNITS.meter\n",
    "joule = UNITS.joule\n",
    "degree = UNITS.degree;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Stage 1: Swing is a pendulum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "#Params Start\n",
    "\n",
    "g = 9.8*m/s**2\n",
    "ChildMass = 40*kg\n",
    "SwingMass = 5*kg\n",
    "StringLength = 2.5*m\n",
    "AngleInit = -(math.pi)/3\n",
    "aVelocityInit = 0/s\n",
    "t_end = 2*s;\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th>values</th>\n",
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       "      <td>g</td>\n",
       "      <td>9.8 meter / second ** 2</td>\n",
       "    </tr>\n",
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       "      <td>ChildMass</td>\n",
       "      <td>40 kilogram</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>SwingMass</td>\n",
       "      <td>5 kilogram</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>StringLength</td>\n",
       "      <td>2.5 meter</td>\n",
       "    </tr>\n",
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       "      <td>AngleInit</td>\n",
       "      <td>-1.0472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>t_end</td>\n",
       "      <td>2 second</td>\n",
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       "      <td>aVelocityInit</td>\n",
       "      <td>0 / second</td>\n",
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      "text/plain": [
       "g                9.8 meter / second ** 2\n",
       "ChildMass                    40 kilogram\n",
       "SwingMass                     5 kilogram\n",
       "StringLength                   2.5 meter\n",
       "AngleInit                        -1.0472\n",
       "t_end                           2 second\n",
       "aVelocityInit                 0 / second\n",
       "dtype: object"
      ]
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     "execution_count": 5,
     "metadata": {
     },
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    }
   ],
   "source": [
    "#Setting params\n",
    "\n",
    "params = Params(g = g,\n",
    "                ChildMass = ChildMass,\n",
    "                SwingMass = SwingMass,\n",
    "                StringLength = StringLength,\n",
    "                AngleInit = AngleInit,\n",
    "                t_end = t_end,\n",
    "                aVelocityInit = aVelocityInit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def make_system(params):\n",
    "\n",
    "    init = State(angle = params.AngleInit, av = params.aVelocityInit)\n",
    "\n",
    "    Child = params.ChildMass\n",
    "    r = params.StringLength\n",
    "    Seat = params.SwingMass\n",
    "    g = params.g\n",
    "    t_end = params.t_end\n",
    "    dt = t_end/100\n",
    "\n",
    "    return System(init=init, Child=Child, r=r, Seat=Seat, g=g, t_end=t_end, dt=dt)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def slope_func(state, t, system):\n",
    "    \"\"\"\n",
    "    Computes derivatives of the state variables.\n",
    "\n",
    "        state: angle, angular velocity\n",
    "        t: time (unused)\n",
    "        system: System object (unused)\n",
    "\n",
    "    returns: derivatives of angle & velocity\n",
    "    \"\"\"\n",
    "    angle, av = state\n",
    "    unpack(system)\n",
    "\n",
    "    dadt = av\n",
    "    davdt = -(system.g*math.sin(angle))/system.r\n",
    "\n",
    "    return dadt, davdt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>init</td>\n",
       "      <td>angle       -1.0472\n",
       "av       0 / second\n",
       "dtype:...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Child</td>\n",
       "      <td>40 kilogram</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>r</td>\n",
       "      <td>2.5 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Seat</td>\n",
       "      <td>5 kilogram</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>g</td>\n",
       "      <td>9.8 meter / second ** 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>t_end</td>\n",
       "      <td>2 second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>dt</td>\n",
       "      <td>0.02 second</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "init     angle       -1.0472\n",
       "av       0 / second\n",
       "dtype:...\n",
       "Child                                          40 kilogram\n",
       "r                                                2.5 meter\n",
       "Seat                                            5 kilogram\n",
       "g                                  9.8 meter / second ** 2\n",
       "t_end                                             2 second\n",
       "dt                                             0.02 second\n",
       "dtype: object"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pendulum = make_system(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": true
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    {
     "data": {
      "text/plain": [
       "(0 <Unit('1 / second')>, 3.3948195828349994 <Unit('1 / second ** 2')>)"
      ]
     },
     "execution_count": 9,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope_func(pendulum.init, 0, pendulum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>angle</th>\n",
       "      <th>av</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0.00</td>\n",
       "      <td>-1.0472</td>\n",
       "      <td>0 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.02</td>\n",
       "      <td>-1.0465185872800307 dimensionless</td>\n",
       "      <td>0.06789639165669999 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.04</td>\n",
       "      <td>-1.0444819618406629 dimensionless</td>\n",
       "      <td>0.135739484746347 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.06</td>\n",
       "      <td>-1.041089275242371 dimensionless</td>\n",
       "      <td>0.20347563188653522 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.08</td>\n",
       "      <td>-1.0363432057837414 dimensionless</td>\n",
       "      <td>0.27105052250649103 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1.92</td>\n",
       "      <td>0.9675624815849634 dimensionless</td>\n",
       "      <td>-0.7265347787380169 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1.94</td>\n",
       "      <td>0.9523861578266541 dimensionless</td>\n",
       "      <td>-0.7907721893986798 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1.96</td>\n",
       "      <td>0.9359319099171372 dimensionless</td>\n",
       "      <td>-0.8542905261401317 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1.98</td>\n",
       "      <td>0.9182148601370111 dimensionless</td>\n",
       "      <td>-0.9170141735552312 / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2.00</td>\n",
       "      <td>0.8992516738645995 dimensionless</td>\n",
       "      <td>-0.9788644043599725 / second</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>101 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  angle                            av\n",
       "0.00                            -1.0472                    0 / second\n",
       "0.02  -1.0465185872800307 dimensionless  0.06789639165669999 / second\n",
       "0.04  -1.0444819618406629 dimensionless    0.135739484746347 / second\n",
       "0.06   -1.041089275242371 dimensionless  0.20347563188653522 / second\n",
       "0.08  -1.0363432057837414 dimensionless  0.27105052250649103 / second\n",
       "...                                 ...                           ...\n",
       "1.92   0.9675624815849634 dimensionless  -0.7265347787380169 / second\n",
       "1.94   0.9523861578266541 dimensionless  -0.7907721893986798 / second\n",
       "1.96   0.9359319099171372 dimensionless  -0.8542905261401317 / second\n",
       "1.98   0.9182148601370111 dimensionless  -0.9170141735552312 / second\n",
       "2.00   0.8992516738645995 dimensionless  -0.9788644043599725 / second\n",
       "\n",
       "[101 rows x 2 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solves differential equation\n",
    "\n",
    "results, details = run_ode_solver(pendulum, slope_func)\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "57.29577951308232 degree"
      ],
      "text/latex": [
       "$57.29577951308232\\ \\mathrm{degree}$"
      ],
      "text/plain": [
       "57.29577951308232 <Unit('degree')>"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Converts radians to degrees\n",
    "\n",
    "rad = (180/math.pi) * degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Results\n",
    "\n",
    "Our model generated a plot of the swing angle vs. time as well as angular velocity vs. time. This graph below shows a good confirmation that we have a model that matches up with the physics of a pendulum. This is because you can see in the graph that when the angle is at 0 the angular velocity is at it highest vs. when the angle is at is highest the av is at zero. This matches up well with what pendulums actually do. We put all of these into a sweep series and used this in the second part of the model. We took each angle and its corresponding av and input them into our projectile model to find the maximum horizontal displacement, which is what we will ultimately be recording to answer our question."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# takes into account pendulum angle in relation to time\n",
    "\n",
    "plot(results.angle, label='angle')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Angle of the pendulum (degrees)')\n",
    "\n",
    "plot(results.av, label='av')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Angular Velocity & Angle (Radians)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Stage 2: Kid is yoted off swing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>x</td>\n",
       "      <td>0 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>y</td>\n",
       "      <td>1 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>g</td>\n",
       "      <td>9.8 meter / second ** 2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mass</td>\n",
       "      <td>40 kilogram</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>angle</td>\n",
       "      <td>45 degree</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>velocity</td>\n",
       "      <td>40.0 meter / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>t_end</td>\n",
       "      <td>20 second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>dt</td>\n",
       "      <td>0.2 second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>r</td>\n",
       "      <td>2.5 meter</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "x                           0 meter\n",
       "y                           1 meter\n",
       "g           9.8 meter / second ** 2\n",
       "mass                    40 kilogram\n",
       "angle                     45 degree\n",
       "velocity        40.0 meter / second\n",
       "t_end                     20 second\n",
       "dt                       0.2 second\n",
       "r                         2.5 meter\n",
       "dtype: object"
      ]
     },
     "execution_count": 13,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_end = 20 * s\n",
    "dt = t_end / 100\n",
    "\n",
    "params = Params(x = 0 * m, \n",
    "                y = 1 * m,\n",
    "                g = 9.8 * m/s**2,\n",
    "                mass = 40 * kg,\n",
    "                angle = 45 * degree,\n",
    "                velocity = 40 * m / s,\n",
    "                t_end=t_end,\n",
    "                dt=dt,\n",
    "                r = 2.5*m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def make_system_2(params):\n",
    "    \"\"\"\n",
    "    Makes a system object.\n",
    "    \n",
    "    params: Params object with angle, velocity, x, y, duration, g,\n",
    "               \n",
    "    returns: System object\n",
    "    \"\"\"\n",
    "    angle, velocity = params.angle, params.velocity\n",
    "    \n",
    "    # convert angle to degrees\n",
    "    theta = angle\n",
    "    \n",
    "    # compute x and y components of velocity\n",
    "    vx, vy = pol2cart(theta, velocity)\n",
    "    \n",
    "    # make the initial state\n",
    "    R = Vector(params.x, params.y)\n",
    "    V = Vector(vx, vy)\n",
    "    init = State(R=R, V=V)\n",
    "    r=params.r\n",
    "    \n",
    "    return System(params, init=init)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def slope_func(state, t, system):\n",
    "    \"\"\"\n",
    "    Computes derivatives of the state variables.\n",
    "    \n",
    "    state: State (x, y, x velocity, y velocity)\n",
    "    t: time\n",
    "    system: System object with mass & g\n",
    "\n",
    "    returns: sequence (vx, vy, ax, ay)\n",
    "    \"\"\"\n",
    "    R, V = state\n",
    "    mass, g = system.mass, system.g\n",
    "    \n",
    "    a_grav = Vector(0, -g)\n",
    "    A = a_grav\n",
    "    \n",
    "    return V, A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def event_func(state, t, system):\n",
    "    \"\"\"\n",
    "    Stops when the y coordinate is 0.\n",
    "    \n",
    "    state: State object\n",
    "    t: time\n",
    "    system: System object\n",
    "    \n",
    "    returns: y coordinate\n",
    "    \"\"\"\n",
    "    R, V = state\n",
    "    return R.y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>success</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>message</td>\n",
       "      <td>A termination event occurred.</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "success                             True\n",
       "message    A termination event occurred.\n",
       "dtype: object"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yeet = make_system_2(params)\n",
    "Results, details = run_ode_solver(yeet, slope_func, events=event_func)\n",
    "details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Results.R, label='travel')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Height?')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(Results.V, label='velocity')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='velocity')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "def range_func(angle, av, params):  \n",
    "    \"\"\"Computes range for a given launch angle.\n",
    "    \n",
    "    angle: launch angle in degrees\n",
    "    params: Params object\n",
    "    \n",
    "    returns: distance in meters\n",
    "    \"\"\"\n",
    "    #print(angle, av)\n",
    "    velocity = av*params.r\n",
    "    params = Params(params, angle=angle, velocity=velocity)\n",
    "    system = make_system_2(params)\n",
    "    results, details = run_ode_solver(system, slope_func, events=event_func)\n",
    "    x_dist = get_last_value(results.R).x\n",
    "    #print(angle, x_dist)\n",
    "    return x_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                  angle                            av\n",
      "0.00                            -1.0472                    0 / second\n",
      "0.02  -1.0465185872800307 dimensionless  0.06789639165669999 / second\n",
      "0.04  -1.0444819618406629 dimensionless    0.135739484746347 / second\n",
      "0.06   -1.041089275242371 dimensionless  0.20347563188653522 / second\n",
      "0.08  -1.0363432057837414 dimensionless  0.27105052250649103 / second\n",
      "...                                 ...                           ...\n",
      "1.92   0.9675624815849634 dimensionless  -0.7265347787380169 / second\n",
      "1.94   0.9523861578266541 dimensionless  -0.7907721893986798 / second\n",
      "1.96   0.9359319099171372 dimensionless  -0.8542905261401317 / second\n",
      "1.98   0.9182148601370111 dimensionless  -0.9170141735552312 / second\n",
      "2.00   0.8992516738645995 dimensionless  -0.9788644043599725 / second\n",
      "\n",
      "[101 rows x 2 columns]\n"
     ]
    }
   ],
   "source": [
    "print (results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-60.000000                     0.0 meter\n",
      "-59.961098     0.03663511721240593 meter\n",
      "-59.844408     0.07142623517042877 meter\n",
      "-59.650022     0.10475769646538338 meter\n",
      "-59.378092     0.13637497223104694 meter\n",
      "                         ...            \n",
      " 55.437247    -0.32336023439252354 meter\n",
      " 54.567707    -0.35057102418493824 meter\n",
      " 53.624948    -0.37839238532743386 meter\n",
      " 52.609836    -0.40698170414764057 meter\n",
      " 51.523326      -0.436484920391761 meter\n",
      "Length: 101, dtype: object\n"
     ]
    }
   ],
   "source": [
    "## From Jason:\n",
    "\n",
    "sweep = SweepSeries()\n",
    "\n",
    "for angle, av in zip(results.angle, results.av):\n",
    "    #print(angle, av)\n",
    "    x_dist = range_func(angle, av, params)\n",
    "    sweep[angle*rad] = x_dist\n",
    "print(sweep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(results.angle, label='angle')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Angle of the pendulum (degrees)')\n",
    "plot(results.av, label='av')\n",
    "\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Angular Velocity & Angle (Radians)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sweep, color='C2')\n",
    "decorate(xlabel='Launch angle (degrees)',\n",
    "         ylabel='Range (m)',\n",
    "         title='Range as a function of launch angle',\n",
    "         legend=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18.793648    2.773540707930243 meter\n",
       "dtype: object"
      ]
     },
     "execution_count": 25,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = sweep.max()\n",
    "sweep[sweep == g]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Interpretation\n",
    "\n",
    "After implementing our sweep, the graph of Range vs. Launch angle shows that the maximum horizontal distance that the child travels after jumping off the swing is between 2.5-3 m, and occurs at an angle of 20 degrees. This makes sense, given that a smaller launch angle will result in a greater horizontal displacement. Also, it seems reasonable to think that a 40kg child will land 3 meters away from the swing, but whether that would be the maximum distance might be up for debate.\n",
    "A limitation of our model lies in the fact that we only accounted for one mass of a child (40 kg), so these particular results would only apply to a child of said mass. In addition, we neglected air resistance and friction caused by the seat of the swing, leading to slight deviations from realistic environments."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
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 },
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 "nbformat_minor": 0
}