A mass M , attached to a horizontal spring, executes S.H.M. with 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 togeth

Question

A mass M , attached to a horizontal spring, executes S.H.M. with 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

Energy of simple harmonic oscillator is constant. ​ ⇒ 2 1 ​ M ω 2 A 1 2 ​ = 2 1 ​ ( m + M ) ω 2 A 2 2 ​ A 2 2 ​ A 1 2 ​ ​ = M M + m ​ ∴ A 2 ​ A 1 ​ ​ = M M + m ​ ​ ​

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