A $0\mathrm{.}540-$kg object attached to a spring with a force constant of $8\mathrm{.}00$ N$/$m vibrates in simple harmonic motion with an amplitude of $13\mathrm{.}0$ cm$.($Assume the position of the object is at the origin at

t $=0.)$

$($a$)$ Calculate the maximum value of its speed.

Have you calculated the angular velocity? You almost always need this quantity for problems involving simple harmonic motion. cm$/$s

$($b$)$ Calculate the maximum value of its acceleration.

Write down the equation for x$($t$)$ and then think about how to find the acceleration as a function of time from this equation. cm$/$s$2$

$($c$)$ Calculate the value of its speed when the object is $9\mathrm{.}00$ cm from the equilibrium position.

Can you determine a time when the object is at this position? You can then use this time in your equation of motion. cm$/$s

$($d$)$ Calculate the value of its acceleration when the object is $9\mathrm{.}00$ cm from the equilibrium position.

How can you determine the force that acts on the object at this position? cm$/$s$2$

$($e$)$ Calculate the time interval required for the object to move from x $=0$ to x $=7\mathrm{.}00$ cm$.$