A 0. 60 kg object rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 23. 5 n/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The object is pushed, and the spring compressed, until xi = −4. 00 cm. it then is released from rest and undergoes simple harmonic motion.
(a) What is the block's maximum speed (in m/s) after it is released?
(b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 1. 60 cm (that is, when x = −1. 60 cm) ?
(c) How fast is the block moving (in m/s) whenever the spring is extended by 1. 60 cm (that is, when passing through x = +1. 60 cm) ?
(d) Find the magnitude of the displacement (in cm) at which the block moves with one-half of the maximum speed.