The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is
IIT 2009, Diffcult
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$F = k _1 x _1 \text { and } F = k _2 x _2$
$\text { tehn } A = x _1+ x _2= F \left(\frac{1}{ k _1}+\frac{1}{ k _2}\right)$
$F =\frac{ k _1 k _2}{ k _1+ k _2} A$
So the amplitude of the point is $x _1=\frac{ F }{ k _1}=\frac{k_2}{k_1+k_2} A$
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