A horizontal spring block system of mass ‘M’ executes SHM of amplitude ‘A’ and frequency 'n'. When the block passes through its equilibrium position, an object of mass ‘m’ is put on it and the two moves together. Find the new amplitude

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A \sqrt{\frac{M}{M + m}}

A \sqrt{\frac{m}{M + m}}

A \sqrt{\frac{m + m}{M}}

A \sqrt{\frac{M + m}{m}}

answer is A.

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Detailed Solution

$f = \frac{1}{2 π} \sqrt{\frac{K}{m}} \to (1)$

$f^{|} = \frac{1}{2 π} \sqrt{\frac{K}{M + m}} \to (2)$

$By L .C .M; m ϑ = (m + M) V$

$V = A ω; ω = 2 π f$

$M (2 π Af) = (M + m) 2 π A^{|} f^{|}$

$MAf = (M + m) A^{|} f^{|} \to (3)$

From (1) & (2) & (3)

$A^{|} = A \sqrt{\frac{M}{M + m}}$

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