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The mass M shown in the figure oscillate...

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

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
Let `x_(1)` and `x_(2)` are maximum elongations produced in the springs when block is at its exteme position then
`x_(1) + x_(2) = A" "…(i)`
Here value of `x_(1)` is amplitude for point P.
both the springs are connected in series and hence same forces is exerted at the ends of springs.
`k_(1)x_(1) = k_(2)x_(2)`
`rArr x_(2) = (k_(1))/(k_(2))x_(1)`
Substituting in equation (i) we get
`x_(1) + (k)(1))/(k_(2))x_(1)= A`
`rArr x_(1) = (k_(2)A)/(k_(1) + k_(2))`
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