Give solution in detail.

Dear Student,

maximum compression occurs when velocity of both blocks are same . {Mv}_{0} = Mv + Mv {Mv}_{0} = 2 Mv v = \frac{v_{0}}{2} By conserving energy, \frac{1}{2} {Mv}_{0}^{2} = \frac{1}{2} {kx}^{2} + \frac{1}{2} M (\frac{{v_{0}}^{2}}{4}) + \frac{1}{2} M (\frac{{v_{0}}^{2}}{4}) \frac{1}{2} M {v_{0}}^{2} = \frac{1}{2} {kx}^{2} + M (\frac{{v_{0}}^{2}}{4}) M (\frac{{v_{0}}^{2}}{4}) = \frac{1}{2} {kx}^{2} \frac{1}{2 k} M {v_{0}}^{2} = x^{2} x = (\sqrt{\frac{M}{2 k}}) v_{0}

Regards