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

Let extensions in the springs be `x_(1)` and `x_(2)`, then `x_(1)+x_(2) =A` and `k_(1)x_(1) = k_(2)x_(2)` Solving, above two equation, we get `x_(1) = (k_(2)A)/(k_(1)+k_(2))`