A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t $=0$ and moves to the right. The amplitude of its motion is $1\mathrm{.}70$ cm$,$ and the frequency is $2\mathrm{.}60$ Hz$.$

$($a$)$ Find an expression for the position of the particle as a function of time. $($Use the following as necessary: t$.$ Assume that x is in centimeters and t is in seconds. Do not include units in your answer.$)$

x $=$

$($b$)$ Determine the maximum speed of the particle.

cm$/$s

$($c$)$ Determine the earliest time $($t $>0)$ at which the particle has this speed

s

$($d$)$ Find the maximum positive acceleration of the particle.

cm$/$s$2$

$($e$)$ Find the earliest time $($t $>0)$ at which the particle has this acceleration.

s

$($f$)$ Determine the total distance traveled between t $=0$ and t $=0\mathrm{.}58$ s$.$

cm