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Question

A body executes SHM under the influence to one force and has time period T1 seconds and the same body executes SHM with period T2 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 is?

A
(T1+T2)sec
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B
T21+T22sec
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C
T1+T2T1T2sec
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D
 T21T22(T21+T22)sec
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Solution

The correct option is D  T21T22(T21+T22)sec
Under the forceF1 time oscillation of the body T1
F1=M(2πT1)2V;whereMisthemassandvisthevelocityandF2=M(2πT2)2V
FNet=F1+F2M(2πT)2=M(2πT1)2+M(2πT2)21T2=1T21+1T22=T21+T22T21T22=T1T2T21+T22

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