A $0\mathrm{.}480-$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 $10\mathrm{.}6$ cm$.($Assume the position of the object is at the origin at

t $=0.)$

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

cm$/$s

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

cm$/$s$2$

$($c$)$ Calculate the value of its speed when the object is $6\mathrm{.}60$ cm from the equilibrium position.

cm$/$s

$($d$)$ Calculate the value of its acceleration when the object is $6\mathrm{.}60$ cm from the equilibrium position.

cm$/$s$2$

$($e$)$ Calculate the time interval required for the object to move from x $=0$ to x $=4\mathrm{.}60$ cm$.$