Question

A mass M attached to a horizontal spring executes S.H.M. of amplitude A₁. 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 A₂. The ratio of `(A_1/A_2)` is ______ 

पर्याय

• `M/(M + m)`

• `(M/(M + m)) 1/2`

• `(M + m)/M`

• `((M + m)/M) 1/2`

Answer 1

A mass M attached to a horizontal spring executes S.H.M. of amplitude A₁. 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 A₂. The ratio of `(A_1/A_2)` is `underline(((M + m)/M) 1/2).`

Explanation:

MV = (M + m)V'

`1/2(M + m)V^{'2} = 1/2kA_2^2`

`1/2MV^2 = 1/2kA_1^2`

`(M + m)/M . V^{'2}/V^2 = A_2^2/A_1^2`

`(M + m)/M . (M/(M + m))^2 = A_2^2/A_1^2`

`A_1^2/A_2^2 = (M + m)/M`

∴ `A_1/A_2 = ((M + m)/m)^{1/2}`