Reference no: EM13294189

Problem #1:

Consider the following initial value problem consisting of two first order ODEs:

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:

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:

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.