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A body executes SHM under the influence ...

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

A

`T_1+T_2`

B

`sqrt(T_1^2+T_2^2)`

C

`sqrt((T_1^2+T_2^2)/(T_1T_2))`

D

`sqrt((T_1^2T_2^2)/((T_1^2+T_2^2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
`T_1=2pisqrt(m/k_1) , T_2=2pisqrt(m/k_2)`
When both the forces are applied simultaneous
`T=2pisqrt(m/(k_1+k_2))=sqrt((T_1^2T_2^2)/(T_1^2+T_2^2))`
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