A$$ cart attached to an ideal spring with a force constant $($spring constant$)$ of$$ oscillates on a horizontal, frictionless track. At time $,$ the cart is released from rest at position$$ from the equilibrium position.

$($a$)$ What is the frequency of the oscillations of the cart?

$($b$)$ Determine the maximum speed of the cart. Where does the maximum speed occur?

$($c$)$ Find the maximum acceleration of the cart. Where does the maximum acceleration occur?

$($d$)$ How much total energy does this oscillating system contain?

$($e$)$ Express the displacement as a function of time using a cosine function.