A spring is resting vertically on a table. A box is dropped onto the top of the spring and compresses it. Assume the spring has a spring constant of 400 N/m and the box has a mass of 1.3 kilogram. The speed of the box just before it makes contact with the spring is 0.58 m/s.
(a) Obtain the magnitude of the spring displacement at an instant when the acceleration of the box is zero.
(b) Obtain the magnitude of the spring displacement when the spring is fully compressed?