Question

The displacement of a particle is represented by the equation `y = 3 cos (pi/4 - 2ωt)`. The motion of the particle is ______.

Options

• simple harmonic with period `(2pi)/ω`

• simple harmonic with period `pi/ω`

• periodic but not simple harmonic

• non-periodic

Answer 1

The displacement of a particle is represented by the equation y = `3 cos (pi/4 - 2 ωt)`. The motion of the particle is `bbunderline("simple harmonic with period" pi/ω)`.

Explanation:

Given: y = `3 cos (pi/4 - 2 ωt)`

y = `3 cos [-(-2 ωt - pi/4)]`   ...[∵ cos(−θ) = cos θ]

= `3 cos(2 ωt - pi/4)`

This matches standard SHM form:

y = A cos (Ωt + Φ)

A = 3

Ω = 2ω

Time period (T) = `(2pi)/Ω`

= (2pi)/(2ω)

= `pi/ω`