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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
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Solution
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`
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