A \(5.0-\mathrm{kg}\) cart is attached to a horizontal spring for which the spring constant is \(75 \mathrm{~N} / \mathrm{m}\). The system is set in motion when the cart is \(0.32 \mathrm{~m}\) from its equilibrium position, and the initial velocity is \(1.5 \mathrm{~m} / \mathrm{s}\) directed towards the equilibrium position.

(a) What is the amplitude of the oscillation?

(b) What is the speed of the cart at the equilibrium position?

(c) What is the speed of the cart at maximum displacement?

(d) How would the answers to parts \(a, b\), and \(c\) change if the initial direction of the motions is directed away from the cart's equilibrium position?