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Questions  

The displacement y of a particle executing periodic motion is given by y=4cos2(t/2)sin(1000t). This expression may be considered to be a result of the superposition of ........... independent harmonic motions

a
Two
b
Three
c
Four
d
Five

detailed solution

Correct option is B

y=4cos2⁡t2sin⁡1000t⇒y=2(1+cos⁡t)sin⁡1000t⇒y=2sin⁡1000t+2cos⁡tsin⁡1000t⇒y=2sin⁡1000t+sin⁡999t+sin⁡1001tIt is a sum of three S.H.M.

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The displacement y of a particle executing periodic motion is given by y=4cos2(t/2)sin(1000t). This expression may be considered to be a result of the superposition of  ........... independent harmonic motions 


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