Damped Harmonic Motion.ipynb

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    "#------------------------------------------------------------*\n",
    "# CHIA E TUNGOM\n",
    "# Dec-06-2019\n",
    "# SZU\n",
    "# Damped Harmonic Motion in PSO\n",
    "#------------------------------------------------------------*"
   ]
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    "# A = amplitude \n",
    "# phi = angle \n",
    "# \n",
    "# K = Force applied to particle\n",
    "# b = resistive force of the environment\n",
    "# m = mass of the particle \n",
    "#\n",
    "#  k, b and m determine the damping frequency of a particle weight and can related as follows\n",
    "#\n",
    "# k = x*m  as x increses, frequency or number of wavelets increases   x[1.0, 10.0]\n",
    "# k = m/x  as x increases, frequency reduces                         \n",
    "# b        as b increases, damping rate increases.    b [0.1, 10] U (5)[10, 25] U (10)[30, 50] U (15)[55, 100]\n",
    "#\n",
    "# m [1,10] or [10,100]         m can be used to determine k as shown in the relation above"
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   "source": [
    "import math\n",
    "\n",
    "\n",
    "# X  = A*math.cos(w*t + phi)*math.exp(-t/ tau)\n",
    "\n",
    "def Motion(w, tau , t = 30, A = 0.4 , phi = 0):\n",
    "    DM = []\n",
    "    for i in range(t):\n",
    "        X = A*(math.cos(w*i + phi))*math.exp(-i/ tau)\n",
    "        #X += A                                       # Shifts X up by A units\n",
    "        DM.append(X)\n",
    "    return DM\n",
    "#--------------------------------------------------------------------------*\n",
    "# Ideal harmonic motion \n",
    "\n",
    "m = 20   # mass of particel\n",
    "k = m/0.1  # force applied to particle\n",
    "b = 5    # existing resitive force\n",
    "A = 0.4    # Amplitide \n",
    "phi = math.pi  # angular velocity\n",
    "\n",
    "tau = (2*m) / b     # time constant\n",
    "\n",
    "w = math.sqrt( (k/m) - (b**2) / ((4*m)**2)) #frequency of oscillation\n",
    "#--------------------------------------------------------------------------*"
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      "[0.4, -0.35292768763258486, 0.31126945025985475, -0.27441767705854486, 0.24183108944030765, -0.21302773418735224, 0.18757868631463318, -0.16510239384987035, 0.14525960263085344, -0.12774880469743363, 0.11230215892090993, -0.09868183718572161, 0.08667675373824581, -0.07609963926652559, 0.06678442489461049, -0.05858390458741298, 0.05136764748772212, -0.04502013446677992, 0.03943909568336946, -0.03453402823255106, 0.030224875041927026, -0.026440848057534792, 0.023119380469063318, -0.020205194269942175, 0.017649470845856965, -0.015409113548294268, 0.013446092349787811, -0.011726861705676233, 0.010221843673591937, -0.008904969175962122]\n"
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    "print(Motion(w, tau))"
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       "            </script>\n",
       "        </div>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.express as px\n",
    "data = Motion(w,tau)\n",
    "px.line(x = [i for i in range(len(data))], y=data, line_shape=\"spline\", render_mode=\"svg\")#range_x=[-10,10], range_y=[-10,10], )"
   ]
  },
  {
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   "execution_count": 16,
   "metadata": {},
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    "#--------------------------------------------------------------------------*\n",
    "# damped harmonic motion \n",
    "m = 20   # mass of particel. \n",
    "k = m/0.1   # force applied to particle. If we used the x factor to determine k, x here will be 1.5     or k = m*1.5\n",
    "b = 0.5    # existing resitive force\n",
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    "phi = math.pi  # angular velocity\n",
    "\n",
    "tau = (2*m) / b     # time constant\n",
    "\n",
    "w = math.sqrt( (k/m) - (b**2) / ((4*m)**2)) #frequency of oscillation\n",
    "#--------------------------------------------------------------------------*\n",
    "import plotly.express as px\n",
    "data = Motion(w,tau)\n",
    "px.line(x = [i for i in range(len(data))], y=data, line_shape=\"spline\", render_mode=\"svg\")#range_x=[-10,10], range_y=[-10,10], )"
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   "source": [
    "#--------------------------------------------------------------------------*\n",
    "# damped harmonic motion \n",
    "m = 20   # mass of particel. \n",
    "k = m/0.1   # force applied to particle. If we used the x factor to determine k, x here will be 1.5     or k = m*1.5\n",
    "b = 10    # existing resitive force\n",
    "A = 0.4    # Amplitide \n",
    "phi = math.pi  # angular velocity\n",
    "\n",
    "tau = (2*m) / b     # time constant\n",
    "\n",
    "w = math.sqrt( (k/m) - (b**2) / ((4*m)**2)) #frequency of oscillation\n",
    "#--------------------------------------------------------------------------*\n",
    "import plotly.express as px\n",
    "data = Motion(w,tau)\n",
    "px.line(x = [i for i in range(len(data))], y=data, line_shape=\"spline\", render_mode=\"svg\")#range_x=[-10,10], range_y=[-10,10], )"
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    "#--------------------------------------------------------------------------*\n",
    "# damped harmonic motion \n",
    "m = 20   # mass of particel. \n",
    "k = 30   # force applied to particle. If we used the x factor to determine k, x here will be 1.5     or k = m*1.5\n",
    "b = 0.9    # existing resitive force\n",
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    "\n",
    "tau = (2*m) / b     # time constant\n",
    "\n",
    "w = math.sqrt( (k/m) - (b**2) / ((4*m)**2)) #frequency of oscillation\n",
    "#--------------------------------------------------------------------------*\n",
    "import plotly.express as px\n",
    "data = Motion(w,tau)\n",
    "px.line(x = [i for i in range(len(data))], y=data, line_shape=\"spline\", render_mode=\"svg\")#range_x=[-10,10], range_y=[-10,10], )"
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       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('eb93d580-7555-49a3-8757-3569d69bf23f');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
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       "    x.observe(outputEl, {childList: true});\n",
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       "            </script>\n",
       "        </div>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.express as px\n",
    "data = Motion(w,tau)\n",
    "px.line(x = [i for i in range(len(data))], y=data, line_shape=\"spline\", render_mode=\"svg\")#range_x=[-10,10], range_y=[-10,10], )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
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   "source": [
    "#--------------------------------------------------------------------------*\n",
    "# underdamped harmonic motion \n",
    "m = 20   # mass of particel\n",
    "k = 30   # force applied to particle     k = m*x     x=1.5\n",
    "b = 15    # existing resitive force\n",
    "A = 0.4    # Amplitide \n",
    "phi = math.pi  # angular velocity\n",
    "\n",
    "tau = (2*m) / b     # time constant\n",
    "\n",
    "w = math.sqrt( (k/m) - (b**2) / ((4*m)**2)) #frequency of oscillation\n",
    "#--------------------------------------------------------------------------*\n",
    "\n",
    "import plotly.express as px\n",
    "data = Motion(w,tau)\n",
    "px.line(x = [i for i in range(len(data))], y=data, line_shape=\"spline\", render_mode=\"svg\")#range_x=[-10,10], range_y=[-10,10], )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
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   "source": [
    "#--------------------------------------------------------------------------*\n",
    "# over-damped harmonic motion \n",
    "m = 20   # mass of particel\n",
    "k = 30   # force applied to particle    m= k*x     x = 1.5\n",
    "b = 70    # existing resitive force\n",
    "A = 0.4    # Amplitide \n",
    "phi = math.pi  # angular velocity\n",
    "\n",
    "tau = (2*m) / b     # time constant\n",
    "\n",
    "w = math.sqrt( (k/m) - (b**2) / ((4*m)**2)) #frequency of oscillation\n",
    "#--------------------------------------------------------------------------*\n",
    "\n",
    "import plotly.express as px\n",
    "data = Motion(w,tau)\n",
    "px.line(x = [i for i in range(len(data))], y=data, line_shape=\"spline\", render_mode=\"svg\")#range_x=[-10,10], range_y=[-10,10], )"
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    "#--------------------------------------------------------------------------*\n",
    "# critically-damped harmonic motion \n",
    "m = 20   # mass of particel\n",
    "k = 30   # force applied to particle       m= k*x     x = 1.5\n",
    "b = 50    # existing resitive force\n",
    "A = 0.4    # Amplitide \n",
    "phi = math.pi  # angular velocity\n",
    "\n",
    "tau = (2*m) / b     # time constant\n",
    "\n",
    "w = math.sqrt( (k/m) - (b**2) / ((4*m)**2)) #frequency of oscillation\n",
    "#--------------------------------------------------------------------------*\n",
    "\n",
    "import plotly.express as px\n",
    "data = Motion(w,tau)\n",
    "px.line(x = [i for i in range(len(data))], y=data, line_shape=\"spline\", render_mode=\"svg\")#range_x=[-10,10], range_y=[-10,10], )"
   ]
  },
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   "outputs": [],
   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
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    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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