The number of independent constituent simple harmonic motions yielding a resultant displacement equation of the periodic motion as `y=8sin^2((t)/(2))sin(10t)` is

Options

A. 8
B. 6
C. 4
D. 3

Answer

D

Explanation

`y=8sin^2((1)/(2))sin(10t)`
`=4[1-cost]sin(10t)` (using `2sin^2(theta)/(2)=1-costheta`)
`=4sin(10t)-4sin(10t)cost`
`=4sin(10t)-2[sin11t+sin9t]`
(using `2sinCcosD=sin(C+D)+sin(C-D))`
`=4sin(10t)-2sin(11t)-2sin(9t)`
Evindently, y is obtained as the superimposition of three independent (i.e., having different anglar frequency `omega`) `SHM`s