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

Case (i) (##JMA_CHMO_C10_010_S01##),
Case (ii) (##JMA_CHMO_C10_010_S02##).
In case (ii), the springs are shown in the maximum compressed by (x_1) and that of spring constant (k_2) is compressed by (x_2) then
`x_1 + x_2 = A` ….(i)
and `k_1 x_1 = k_2 x_2 rArr x_2 = (k_1 x_1)/(k_2)` ....(ii)
From (i) & (ii)
`x_1 + (k_1 x_1)/(k_2) = A rArr x_1 = (k_2 A)/(k_2 + k_1)`.