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The displacement of a particle in a peri...

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

A

two

B

three

C

four

D

five

Text Solution

Verified by Experts

The correct Answer is:
B
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
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