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

Options

A. two
B. three
C. four
D. five independent harmonic motions.

Answer

B

Explanation

`y=4cos^(2)(t//2)sin 1000t`
`=2(1+cost) sin 1000t`
`( :' 2 cos^(2)theta=1+cos2theta)`
`=2sin 1000t + 2 sin 1000t cost `
`=2sin 1000t + 2 sin (1000+1)t+sin (1000-1)t`
`[ :' sin A cos B=sin (A+B)+sin (A-B)]`
`=2sin 1000t + sin 1001 t + sin 999 t`
This shows that the given expression is the result of three independent harmonics.