Solve the equation of motion,

\[ \ddot{x}+x=\frac{1}{m} F(t) \]

for:

(a) \(F(t)=\cos 0.5 t\),

(b) \(F(t)=\cos 0.99 t\),

(c) \(F(t)=\cos t\), and

(d) \(F(t)=\cos 2 t\). Plot the responses and compare the results. Let \(m=1\) with appropriate units.