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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) (t)/(2) 1000 t`
How many independent harmonic motions may be considered to superpose to results this expression :

Text Solution

Verified by Experts

`y=4cos^(2)(t/2)sin(1000t)`
`y=2[1+cost]sin 1000t`
`[2cos^(2) theta =(1+cos^(2)theta)]`
`y=2sin 1000 t+2sin 1000 t.cos t`
`y=2sin 1000 t+sin 1001t+sin 999t`
[as `2 sin A cos B=sin(A+B)+sin(A-B)`
`:. `The given expression is the resultant of three independent simple harmonic motion.
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