Q$3(35$ pts$)$: A spring having a stiffness coefficient of k N$/$m is compressed L meter and then released to push a block of m kg up the inclined plane. The block reaches its maximum height at point A$,$ then moves back down the plane and compresses the spring again. Calculate;

a$)$ The maximum height $($hmax$)$ the block attains.

b$)$ The maximum contraction of the spring when the object compresses the spring. The coefficient of kinetic friction between the block and the inclined plane is

The horizontal path is frictionless and much longer than the length of the spring.

Hint: Friction force should be taken into account twice, namely in both upward and downward direction motions.