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

Answer

B

Explanation

The given equation can be written as
`y=2(2"cos"^(2)(t)/(2))sin(1000t)`
`y=2(2cost+1)sin(1000t)`
`=2costsin1000t+2sin(1000t)=sin(1001t)+sin(999t)+2sin(1000t)`
i.e., the given expression is a result of superposition of three independent harmonic motions of angular frequencies 999,1000 and 1001 rad/s