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

Refer to figure, Here the two springs are in series. Let the mass `M` be pulled through small distance `A` towards right hand side. Due to it, let `x_(1)` and `x_(2)` be the extension in two springs.
Here, the tnesion or the force is same for both the springs. So `k_(1)x_(1)=k_(2)x_(2)` or `x_(2=k_(1)x_(1)//k_(2)`.
Total extension, `A=x_(1)+x_(2)`
`=x_(1)+(k_(1)x_(1))/(k_(2))=x_(1)((k_(2)+k_(1))/(k_(2)))`
`:.` Amplitude of point `P=` extension of spring `k_(1)`
`=x_(1)=(k_(2)A)/(k_(1)+k_(2))`