Forced oscillations and resonance

A mass of 4 kg on a spring with $k=4 N/m$ and a damping constant $c=1 Ns/m$. Suppose that $F_0 = 2 N$. Using the forcing function $F_0 \cos (\omega t)$, find the $\omega$ that causes practical resonance and find the practical resonance amplitude.

Derive a formula for $x_{sp}$ for $mx''+cx'+kx = F_0 \cos(\omega t) + A$, where $A$ is some constant. Assume $c > 0$.

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 $t=0$.