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 = 4 cos^(2) ((t)/(2))sin (1000t)`
`y = 2[1 + cost] sin 1000t [ :' 2 cos^(2) theta=(1+cos 2 theta)]`
`y = 2 sin 1000 t+2 sin 1000t cos t`
`y = 2 sin 1000t + sin 1001 t+ sin 999t`
`[as 2sin A Cos B +Sin (A+B) +Sin (A-B)]`
`:.` The given expression is the resultant of three independent simple harmonic oscillations