Question $3$: If $x(t)=$Acos$(t)+$Bsin$(t)$ :

Show that $x(t)$ satisfies the spring equation, $m{x}^{}(t)=-kx(t).$

What is the initial position and initial velocity? Rewrite $x(t)$ using this result.

Question $4$: If $x(t)=$Acos$(t+)$ :

$-$What is the angular frequency equal to$?$

If the initial velocity is zero and the initial position is $5$ cm $,$ what is the amplitude and phase?

EXTRA CREDIT: If the initial velocity is $5c\frac{m}{s}$ and the initial position is $0$ cm $,$ what is the amplitude and phase?