Create a MATLAB program to simulate motion of a pendulum in 2-D. The pendulum is a uniform slender rod with its upper end inertially fixed with a frictionless pin joint. Use Euler integration to solve the equation of motion. The pendulum should have a length of 1 meter and a mass of 5 kg.

1. Plot and animate the motion of the pendulum for 5 seconds using an initial angle of 40 degrees and initial angular velocity of 0 deg/sec. You will need to determine dt such that the pendulum motion is as expected.

2. Vary the time step until the pendulum becomes unstable. Plot and animate the motion. How does this compare to the motion simulated in #1 above? Why does this happen?

Include a separate MATLAB code for each part. Each code should have an animation and a plot of angle as a function of time. Include and descriptive answer at the bottom of the related code (don't forget to comment out).