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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 2p/w.
simple harmonic with period π/ω.
periodic but not simple harmonic.
non-periodic.
Solution
The displacement of a particle is represented by the equation `y = 3 cos (pi/4 - 2ωt)`. The motion of the particle is simple harmonic with period π/ω.
Explanation:
When a force (called the restoring force) proportional to the displacement acts on a particle, it produces a simple harmonic motion. In nature, all sine and cosine functions of t are simple harmonics. As a result, the movement is a simple harmonic motion. A simple harmonic motion is always periodic. Hence the motion is simply harmonic with the time period `π/ω`.
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