Problem #1:
Consider the following initial value problem consisting of two first order ODEs:
![936_System for second order Runge-Kutta.png](https://secure.tutorsglobe.com/CMSImages/936_System%20for%20second%20order%20Runge-Kutta.png)
On the domain 0< x <3
A.) solve the system using Euler's Method for h = 0.25; h = 0.1
B.) solve the system for second order Runge-Kutta (modified Euler) for h= 0.25; h = 0.1
Problem #2: damped non-linear ODE
A pendulum is modeled by a mass attached to a weightless rigid rod. By Newton's 2nd Law:
![1348_System for second order Runge-Kutta1.png](https://secure.tutorsglobe.com/CMSImages/1348_System%20for%20second%20order%20Runge-Kutta1.png)
Where theta is the angle of the pendulum with respect to vertical axis, the damping coefficient is c = 0.16 (N*s)/m, and m = 0.5 kg. The length of the rod is L= 1.2m and g is the acceleration due to gravity.
One can re-write the governing equation as follows:
![1297_System for second order Runge-Kutta2.png](https://secure.tutorsglobe.com/CMSImages/1297_System%20for%20second%20order%20Runge-Kutta2.png)
Consider the problem where the initial displacement is theta = 90 degrees at time equal to zero.
Determine the angle of the pendulum as a function of time for the first 18 seconds after release.