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The mass (M) shown in the figure oscilla...

The mass (M) shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point (P) .`
(##JMA_CHMO_C10_010_Q01##).`

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))`

Text Solution

Verified by Experts

The correct Answer is:
D
In series force remain same, if extension in `k_(1)` and `k_(2)` are `x_(1)` and `x_(2)` respectively.
Then `k_(1)x_(1) = k_(2)x_(2)rArr x_(1)+x_(2) = A`
`rArr x_(1) + (k_(1)x_(1))/(k_(2)) = A rArr x_(1) (k_(1) + k_(2))/(k_(2)) = A`
`rArr x_(1) = (k_(2)A)/((k_(1) + k_(2)))`
Amplitude of point P will be the max, ext. in `k_(1)`.
So amplitude of point P is `(k_(2)A)/(k_(1)+k_(2))`
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