A mass M attached to a horizontal spring executes S.H.M. of amplitude A 1 . When the mass M passes through its mean position, then a smaller mass m is placed over it and both of them move together w

Question

A mass M attached to a horizontal spring executes S.H.M. of amplitude A 1 ​ . 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 2 ​ A 1 ​ ​ ) is

TestHub · Accepted Answer

M V = ( M + m ) V ′ 2 1 ​ ( M + m ) V ′2 = 2 1 ​ k A 2 2 ​ 2 1 ​ M V 2 = 2 1 ​ k A 1 2 ​ M M + m ​ ⋅ V 2 V ′2 ​ = A 1 2 ​ A 2 2 ​ ​ M M + m ​ ⋅ ( M + m M ​ ) 2 = A 1 2 ​ A 2 2 ​ ​ A 2 2 ​ A 1 2 ​ ​ = M M + m ​ ∴ A 2 ​ A 1 ​ ​ = ( M M + m ​ ) 2 1 ​

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