Question

A mass `M` attached to a horizontal spring executes `SHM` with an amplitude `A_(1)`. When mass `M` passes through its mean position a smaller mass `m` is placed over it and both of them move togther with amplitude `A_(2)`. Ratio of `((A_(1))/(A_(2)))` is:

Answer 1

`T_(1) = 2pi sqrt((M)/(k)), T_(2) = 2pi sqrt(((m+M))/(k))`
Using, law of conservation of linear momentum
`MV_(1) =(m+M) V_(2)`
`M (A_(1) omega_(1)) =(m +M) (A_(1)omega_(2))`
`(A_(1))/(A_(1)) = ((m+M))/(M) (omega_(2))/(omega_(1)) = ((m+M))/(M) xx (T_(1))/(T_(2))`
`(A_(1))/(A_(2)) = sqrt((m+M)/(M))`.