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The displacement y of a particle executi...

The displacement `y` of a particle executing periodic motion is given by `y = 4 cos^(2) ((1)/(2)t) sin(1000t)`
This expression may be considereed to be a result of the superposition of

A

two moves

B

three moves

C

four moves

D

five moves

Text Solution

Verified by Experts

If we have a term `cos kx sin omegat`, it is the superposition of two wave motions. If we have an equation of the form `cos^(2)` at `sinbt` it can be shown to be superposition of three sine waves.
Here, `y=4cos^(2)((1)/(2)t sin(1000)t)`
`=2[1+cost]sin1000t=2[sin1000t+(1)/(2)(sin100t+sin999t)]=` this comprises three waves.
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