Exercise 103

Suppose there is no damping in a mass and spring system with $m = 5 kg$, $k= 20 N/m$, and $F_0 = 5 N$. Suppose $\omega$ is chosen to be precisely the resonance frequency.

1. Find $\omega$.
2. Find the amplitude of the oscillations at time $t=100$ seconds, given the system is at rest at $t=0$.