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Question

# A body executes SHM under the influence of one force and has a period T1 seconds and the same body executes SHM with period T2 second 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 is:

A
(T1+T2)sec
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B
T21+T22
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C
T21+T22T1T2sec
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D
T21T22(T21+T22)sec
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Solution

## The correct option is D √T21T22(T21+T22)secGiven:- Time oscillation of the body = T1 Time oscillation of the body = T2To find:- The time period of the same body Solution:-Under the force F1 time oscillation of the body T1F1=M(2πT1)2Vwhere M is th emass and v is the velocityandF2=M(2πT2)2VFNet=F1+F2M(2πT)2V=M(2πT1)2V+M(2πT2)2V1T2=1T21+1T221T2=T21+T22T21×T221T= ⎷T21T22T21+T22sec Hence the correct option is D

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