In the arrangement shown, the blocks are pulled apart by 3 cm and released. If maximum velocity of 1 kg block is 1 m/s, what is the maximum velocity of 2 kg block?

The blocks will oscillate with same angular frequency ω. If amplitudes of oscillation of 2 kg and 1 kg blocks are A1 and A2 respectively, then 2×A1=1×A2 as centre of mass of the blocks does not move. Now (V2)max⁡(V1)max⁡=ω.A2ω.A1=2∴ (V1)max⁡=12ms