$4\mathrm{.}8(19$ pts$.)$ System identification for an unstable se

The linearized equation of motion for the unstable

sailboat shown right is

$\backslash$theta $^()-$h$\backslash$theta $=0,($ h is a positive constant$)$

Determine the analytical solution for $\backslash$theta $($t$)$ when

$\backslash$theta $(0)=0\mathrm{.}2\backslash$deg and $\backslash$theta $^()(0)=0$h$,$ and t $\backslash$theta $($t$)=$

Graphed right is this ODE's solution for $\backslash$theta $($t$).$

Estimate the numerical value of h$\backslash$sqrt$(),$ sin$,$ in$,$ exp$[$ numerical value of h in terms of $],[$ tor functions $($eg$.$t$\backslash$sqrt$(1)$ sin$,$ In$,$ exp$).],[$h~~$200,]$