This problem is an example of critically damped harmonic mostion.

A mass m $=81kg$ is amached to bodh a spring with spring comant $k=392\frac{N}{m}$ and a dahh$-$por with damping comant $e=112N*\frac{s}{m}.$ The ball is started in movion with initial position $x_0=2m$ and initial velociry $t_0=-18\frac{m}{s}.$

Determine the position fonction $a(t)$ in metern.

$x(t)=$

Graph the function $a(t).$ find the pointion fanction w$($t$).$

In this case the position function $u(t)$ can be written as $w(t)=C_{\text{c}\text{r}\text{o}\text{s}}(t-a_0).$ Determine $C_2,$ up and $a_0$