Suppose you attach the object with mass m to a vertical spring originally at rest, and let it bounce up and down. You release the object from rest at the spring's original rest length.

(a) Show that the spring exerts an upward force of 2.00 mg on the object at its lowest point. 

(b) If the spring has a force constant of 10.0 N/m and a 0.25-kg-mass object is set in motion as described, find the amplitude of the oscillations. 

(c) Find the maximum velocity.