A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N m-1. A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together find the frequency and the amplitude of the motion.
At the mean position, let 1kg block has velocity v.
After the 3kg block is gently placed on the 1kg, then 1kg+3kg=4kg block and the spring be one system. For this mass spring system, there is external force, the momentum should be conserved. Let 4kg block has velocity V.
Therefore initial and final momentum should be equal.
Now the two blocks have velocity 1/4 m/s at its mean position.
When the blocks are going to the extreme position, there will be only potential energy, (X new amplitude)