A block of mass m rests on a rough plane inclined at with the horizontal (Figure).

A block of mass m rests on a rough plane inclined at θ with the horizontal (Figure). The block is attached to a spring of constant k near the top of the plane. The coefficients of static and kinetic friction between the block and plane are µs and µk, respectively. The spring is slowly pulled upward along the plane until the block starts to move. 

(a) Obtain an expression for the extension d of the spring the instant the block moves.

(b) Determine the value of µ_k such that the block comes to rest just as the spring is in its unstressed condition, i.e., neither extended nor compressed.