In the figure shown, the block A of mass m collides with the identical block B and after collision they stick together. Calculate the amplitude of resulatant vibration.

Explanation

Common velocity after collision`= (u)/(2)`
Hence, `K.E. = (1)/(2) (2 M) ((u)/(2))^(2) = (1)/(4) Mu^(2)`
It is also total energy of vibration because the string is unstretched at this moment, hence, if A is the amplitude , then
`(1)/(2) KA^(2) = (1)/(4) Mu^(2) or A = sqrt((M)/(2 K)) u`