In the figure above, an object of mass M = 2.1 kg is dropped from a distance h = 0.43 meter above an uncompressed spring. The spring has a constant of k = 210 N/m. The object becomes attached to the spring upon collision. (a)  Calculate the speed of the object when it collides with the spring.

(b)  Determine how far the spring has moved when the object reaches maximum speed.

(c)   On the grid below make a graph of the acceleration a of the block as a function of time t for two oscillations. The horizontal axis is scaled for the values of time T and 2T where T is the period of oscillation. Let t = 0 when the object is at its lowest position.

(d)  On the grid below make a graph of the kinetic energy K of the block as a function of time t for two oscillations. The horizontal axis is scaled for the values of time T and 2T where T is the period of oscillation. Let t = 0 when the object is at its lowest position.

(e)  Describe how the period of oscillation of the object could be changed to one-half its current value. Explain your reasoning.