A mass M, attached to a horizontal spring, executes SHM with amplitude When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude` A_(2)` The ratio of` (A_(1)/A_(2))` is :

Explanation

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