The spring is compressed by a distance $a$  and released.  The block again comes to rest when the spring is elongated by a distance  $b.$  During this :

Using work energy theorem
$W_{net}=rk$
$W_f+W_{sp}=K_f-K_i$
$-\mu Mg(a+b)+\frac{1}{2}k(a^2-b^2)=0$
$\boxed{\mu =\frac{k(a-b)}{2Mg}}$
Potential energy stored in spring 
Initially $U_i=\frac{1}{2}K{a}^2$
Finally  $U_f=\frac{1}{2}K{b}^2$
Work done by spring $=U_i-U_f$

$=\frac{1}{2}K(a^2-b^2)$