In the system below, a block with mass m is set against a spring with spring constant k. The spring is compressed a distance d from its equilibrium point and released from rest. The dark part of the surface has a coefficient of friction μk. After the block travels a distance L, the surface becomes frictionless. The block then travels up the curved part of the track and reaches some maximum height h.
a) Find an expression for the spring compression d required for the block to reach height h, given h, L, k, and g.
b) Find the spring compression d required to double the final maximum height. Your answer should be in terms of the original spring compression d and numerical constants only.