Question

A particle performs simple harmonic motion with period of 3s. The time taken by It to cover a distance equal to half the amplitude from mean position is [sin 30° = 0.5]

Options

• `1/4`s

• `3/2`s

• `3/4`s

• `1/2`s

Answer 1

`1/4`s

Explanation:

The displacement of particle in SHM at any instant,

x = A sin ωt

`"A"/2` = A sin ωt   ...`("given", x = "A"/2)`

sin ωt = `1/2 = sin  pi/6 => ωt = pi/6`

`=> (2pi)/"T" * "t" = pi/6  ...(because omega = (2pi)/"T")`

`=> (2pi)/3 "t" = pi/6    ...(because "T" = 3"s")`

`=> "t" = 1/4`s