The mass (M) shown in the figure oscillates in simple harmonic motion with amplitude of the point (P) is.

Question

The mass (M) shown in the figure oscillates in simple harmonic motion with amplitude of the point (P) is.

The mass (M) shown in the figure oscillates in simple harmonic motion with 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))`

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - 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))`