Question

A body executes SHM under the influence of one force and has a time period of \(T_1\) seconds. The same body executes SHM with a time period of \(T_2\) seconds under the influence of another force separately. When both forces act simultaneously and in the same direction, then the time period of the body is

• A. \[ (T_1+T_2)\ \text{sec} \]
• B. \[ \sqrt{T_1^2+T_2^2}\ \text{sec} \]
• C. \[ \sqrt{\frac{T_1+T_2}{T_1T_2}}\ \text{sec} \]
• D. \[ \sqrt{\frac{T_1^2T_2^2}{T_1^2+T_2^2}}\ \text{sec} \]

Hint:

When two restoring forces act simultaneously, \[ k_{\text{eff}}=k_1+k_2. \] Using \[ T=2\pi\sqrt{\frac{m}{k}}, \] one gets \[ \frac1{T^2} = \frac1{T_1^2} + \frac1{T_2^2}. \]

Answer 1

The Correct Option is D