A particle moving along the x axis in simple harmonicher leaving the motion. Her ovmotion starts from its equilibrium position, the origin, atfree fall and at $=0$ and moves to the right. The amplitude of its motion is$($a$)$ For the fr$2\mathrm{.}00$ cm$,$ and the frequency is $1\mathrm{.}50$ Hz$.($a$)$ Find an expres$-$model to descrsion for the position of the particle as a function of time.in free fall? $($c$)$Determine $($b$)$ the maximum speed of the particle andplunge, is the$($c$)$ the earliest time $($t $>0)$ at which the particle has thisthe Earth isolspeed. Find $($d$)$ the maximum positive acceleration of thepart $($c$)$ find $1$particle and $($e$)$ the earliest time $($t $>0)$ at which the parti$-$is the locaticle has this acceleration. $($f$)$ Find the total distance traveledforce balanc$($f$)$ What is tby the particle between t $=0$ and t $=1\mathrm{.}00$ s$.$