The mass M shown in figure ocillates 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

A

Explanation

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)andx_(2)` be the extension in two springs.
When two springs are in series, the tension or the force is same for both the springs. So `k_(1)x_(1)=k_(2)x_(2)orx_(2)=(k_(1)x_(1))/(k_(2))`
Total extension, `A=x_(1)+x_(2)=x_(1)+(k_(1)x_(1))/(k_(2)),A=x_(1)((k_(2)+k_(1))/(k_(2)))`
`therefore` Amplitude of point P = extension of spring `k_(1)`
`=x_(1)=(k_(2)A)/(k_(1)+k_(2))`