The displacement of a particle from its mean position (in mean is given by `y = 0.2 sin(10pi t + 1.5 pi) cos (10 pi t+ 1.5 pi)`. The motion but not `S.H.M.`

Options

A. periodic but not SHM
B. non periodic
C. simple harmonic motion with period 0.1 s
D. simple harmonic motion with period 0.2 s

Answer

B

Explanation

Given, `y = 0.2 sin (10 pi t + 1.5 pi)cos(10 pi t + 1.5 pi)`
`y = 0.1 sin 2(10 pi t + 1.5 pi) " "["using, 2 sin A cos A"=sin 2 A]`
`y = 0.1 sin (20 pi t + 3 pi)`.
This equation represents simple harmonic motion of angular frequency `20 pi`.
`therefore` Time period, `T = (2pi)/(omega) = (2 pi)/(20 pi) = (1)/(10) = 0.1`