Question

The displacement of a particle from its mean position (in metre) is given by, y = 0.2 sin(10 πt + 1.5π) cos(10 πt + 1.5π).

The motion of particle is ____________.

Options

• periodic but not S.H.M

• non-periodic

• simple harmonic motion with period 0.1 s

• simple harmonic motion with period 0.2 s

Answer 1

The displacement of a particle from its mean position (in metre) is given by, y = 0.2 sin(10 πt + 1.5π) cos(10 πt + 1.5π).

The motion of particle is simple harmonic motion with period 0.1 s.

Explanation:

`y = 0.2 sin(10 pit + 1.5 pi) cos( 10 pit + 1.5 pi)`

`= 0.1 sin2(10 pit + 1.5 pi)   ......[ because sin2A = 2 sinA cosA]`

`= 0.1 sin(20 pit + 3.0 pi)`

`therefore  "Time period", T = (2pi)/omega= (2pi)/(20pi) = 1/10 = 0.1 s`