The displacement of a particle in a periodic motion is given by `y=4 "cos"^(2)(t//2)"sin"(1000t)` . This displacement may be considered as the result superposition of n independent harmonic oscillations. Here , n is

Options

A. two
B. three
C. four
D. five

Answer

B

Explanation

`y =4 cos^(2)((t)/(2))sin(1000 t)`
`=2(cos^(2)(t)/(2)sin 1000 t)`
`=2[cos t+1]sin 1000t = 2 cos t sin 1000t + 2 sin 1000 t`
`= sin 1001 t+ sin 999t +2 sin 1000 t`.