The displacement of a particle executing SHM is given by `y=cos^(2)(t//2)sin(1000t).` Finid the independent constituent SHM's.

Explanation

`y=4cos^(2)(t//s)sin(1000t)`
`=2(1+cost)sin(1000t)`
`[:' cos 2theta=2cos^(2)(theta-1)]`
`=2sin(1000t)+2sin(1000t)cost`
`=2sin(1000t)+sin[(1000t+t)+sin(1000t-t)]`
`[:'2sinA cosB=sin(A+B)+sin(A-B)]`
or `y=2sin(1000t)+sin(10001t)+sin(999t)`
It means this motion is a combination of three independent SHMs, which are
`sin(1000t),sin(1001t) and sin(999t)`