From 1bd154b05401effa3c4e8ae0beff230e984519e0 Mon Sep 17 00:00:00 2001
From: Swarali-glitch <71065651+Swarali-glitch@users.noreply.github.com>
Date: Mon, 19 Oct 2020 11:32:08 +0530
Subject: [PATCH] Create RungeKutta_FreeFall.py

This Python program numerically solves the equation of motion of a free falling object acted on by air drag using the 4th order Runge-Kutta method. We find the velocity of the object as a function of time and plot it.
---
 RungeKutta_FreeFall.py | 44 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 44 insertions(+)
 create mode 100644 RungeKutta_FreeFall.py

diff --git a/RungeKutta_FreeFall.py b/RungeKutta_FreeFall.py
new file mode 100644
index 0000000..d5c3d8c
--- /dev/null
+++ b/RungeKutta_FreeFall.py
@@ -0,0 +1,44 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+m = 0.01
+k = 0.0001
+g = 10
+
+steps = 10  # You can change the number of steps you want to divide interval into
+
+v = np.zeros(steps, dtype = float)
+
+def DE(t,v):
+  return (g-(k*pow(v,2)/m))
+
+
+def RungeKutta(t_0, v_0, t, h):
+  n = int((t-t_0)/h)
+  v = v_0
+  for i in range(1,n+1):
+    s1 = h * DE(t_0, v)
+    s2 = h * DE(t_0+(h/2),v +(s1/2))
+    s3 = h * DE(t_0+(h/2),v +(s2/2))
+    s4 = h * DE(t_0+h, v+s3)
+
+    v = v + (1/6)*(s1+ (2*s2) + (2*s3) + s4)
+    t_0 = t_0 + h
+  return v
+
+t_0 = 0
+v_0 = 0
+t = np.linspace(0,10,num=steps)
+
+for i in range(0,steps):
+  v[i] = RungeKutta(t_0, v_0, t[i], 0.2)
+
+print(t)
+print(v)
+
+fig,ax = plt.subplots()
+ax.plot(t,v)
+ax.set(xlabel='time (s)', ylabel='velocity (m/s)',
+       title='velocity vs. time for particle falling under gravity acted by air drag')
+ax.grid()
+plt.show()