SHM DOUBT

v_cm = m₁v₀ / m₁ + m₂
k.e. of the centre of mass = K=1/2 (m₁ + m₂ ) v_cm²
energy of the 2 blocks is E= 1/2 m₁v₀²
mathematically we see that E>K_CM..this difference is the energy of vibration !
thus E_VIB = E - K_CM
at maximum compression of the spring the whole of the vibrational energy is the elastic potential energy of the spring
=> 1/2 k x_m² = E_VIB => x_m = √2 E_VIB /K
...now its a cakewalk !