The mass `M` shown in the figure oscillates in simple harmnonic motion and amplitude `A`. The amplitude of the point `P` is

Options

A. `(k_(1)A)/(k_(2))`
B. `(k_(2)A)/(k_(1))`
C. `(k_(1)A)/(k_(1) + k_(2))`
D. `(k_(2)A)/(k_(1) + k_(2))`

Answer

D

Explanation

Extensions in springs are `x_(1)` and `x_(2)` then
`k_(1)x_(1) = k_(2)x_(2)`
and `x_(1) + x_(2) = A`
`rArr x_(1) + (k_(1)x_(1))/(k_(2)) = A rArr x_(1) = (k_(2)A)/(k_(1) + k_(2))`