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 1000t`
`=2 "cos"(t)/(2)[sin(1000+(1)/(2))t+sin(1000-(1)/(2))t]`
`=sin1001 t+sin1000t+sin 1000t+sin 999t`
`=sin 1001t+2 sin 1000t+sin 999t`