Example $23-3$: Spring is started with a push. Suppose the spring of Example $23-2($where $=8\mathrm{.}08$ s$-1)$ is compressed $0\mathrm{.}100$ m from equilibrium $($x$0=-0\mathrm{.}100$ m$)$ but is given a shove to create a velocity in the $+$x direction of v$0=0\mathrm{.}400$ m$/$s$.$ Determine $($a$)$ the phase angle $,($b$)$ the amplitude A$,$ and $($c$)$ the displacement x as a function of time, x$($t$)$