Question

A body in SHM has time period $T_1$ seconds under influence of one force and the same body executes SHM with period $T_2$ seconds under the influence of another force. Find the time period (in s) of the same body when both forces act simultaneously in the same direction.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$F_1=\frac{-4{\pi }^2}{T_1^2}x$
$F_2=\frac{-4{\pi }^2}{T_2^2}x$
$\Rightarrow F_1+F_2=-4{\pi }^2(\frac{1}{T_1^2}+\frac{1}{T_2^2})x$
$=\frac{-4{\pi }^2}{T^2}x$
$\therefore T=\sqrt{\frac{T_1^2{T}_2^2}{T_1^2+T_2^2}}$