Question

# The displacement of a particle is represented by the equation y=3 cos (π4−2ωt). The motion of the particle is

A
Simple harmonic with period 2πω
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B
Simple harmonic with period πω
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C
Periodic but not simple harmonic
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D
Non-periodic
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Solution

## The correct option is B Simple harmonic with period πωGiven, y=3 cos(π4−2ωt) Velocity , v=dydt=3×2ω sin(π4−2ωt) Acceleration, a=dvdt=−12ω2 cos(π4−2ωt) ⇒a=−4ω2y As, a∝y and negative sign shows that it is directed towards equilibrium (or mean position), hence particle will execute SHM. y=3 cos(π4−2ωt)=3 cos(2ωt−π4) Comparing above with equation y=rcos (ω′t+ϕ), we have ω′=2ω 2πT′=2ω ⇒T′=πω

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