**Class 3: Numerical Solutions of Ordinary Differential Equations**

** Problem (8.2): Euler & 4th Order RK solutions to SHM**

Performance of both methods with varying step size:

Python source for Euler method

Python source for 4th order RK method

** Problem (8.3): 4th order Runge-Kutta adaptive stepper**

Chosen step size as desired local error varies:

Python source for 4th order Runge-Kutta adaptive stepper

** Problem (8.4): Numerical Solution for pendulum for periodic support motion**

Solved with the RK adaptive stepper form the previous problem. Gravity = 10, length = 1, desired local error = 0.0001

**Solution not animated. Consider animating it and posting a video**

Solution with with amplitude = 6 and frequency = 2:

Solution with with amplitude = 6 and frequency = 1: