The displacement of a particle from its mean position (in metre) is given by
`y=0.2 "sin" (10 pi t+ 1.5 pi) "cos" (10 pi t+1.5 pi)`
The motion of the particle is

Options

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

Answer

C

Explanation

`x=0.2sin(10pit+1.5pi)cos(10pit+1.5pi)`
`=0.2xx(1)/(2)sin2(10pit+1.5pi)(becausesin2theta=2sinthetacostheta)`
`0.1 sin(20pit+3pi)" "...(i)`
Comparing (i) with `x=Asin(omegat+phi)`, which is the equation of SHM, we get
`omega=20pi or (2pi)/(T)=20pi or T=0.1s`
The given equation represents SHM with period of 0.1 s.