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

Explanation

`y=cos^(2)(t//2)sin(100t)`
`=2(1=cost)sin(100t)`
`[ :'cos2theta =2cos^(2)theta-1]`
`=2sin100t+2sin100tcost`
`=2sin100t+sin(100+1)t`
`+sin(100-1)t`
`=2sin100t+sin101t+sin99t`
` :'2sinAsinB=sin(A+B)+sin(A-B)]`
Thus, the given expression is the resultant of three independent harmonics.