$4.[10$ Marks$]$ The diagram shows a $\backslash (0\mathrm{.}300-\backslash$mathrm$\{$kg$\}\backslash )$ block connected to a spring oscillating back and forth at $\backslash (\backslash$mathrm$\{$t$\}=0\backslash )$ where $\backslash (\backslash$mathrm$\{$A$\}=0\mathrm{.}10\backslash$mathrm$\{$~m$\}\backslash ).$ The period is $0\mathrm{.}750$ seconds.

$($a$)$ Sketch the reference circle and indicate object location for the current situation.

$($b$)$ Find the phase constant $\backslash (\backslash$phi$\_\{0\}\backslash )$ in degrees and radians.

$($c$)$ Sketch the $\backslash ($ x$-$t $\backslash )$ and $\backslash ($ v$-\backslash$mathrm$\{$t$\}\backslash )$ graphs. Label axes!

$($d$)$ What is the spring constant K $?$

$($e$)$ How long will it take to reach equilibrium from the instant shown? $($Hint $-$ one full rotation of a reference circle is equal to one complete period. Where is equilibrium on the reference circle you drew?$)$