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  • Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure.

The figure shows the circular motion of a particle. The radius of the circle, the period, the sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is

(a)x(t)=Bsin⁡(2πt30)

(b) x(t)=Bsin⁡(πt15)
(c) x(t)=Bsin⁡(πt15+π2)
(d)x(t)=Bcos⁡(πt15+π2)

Answers (1)

Given: T=30s, OQ=B.

The projection of the radius vector on the diameter of the circle when a particle is moving with uniform angular velocity (ω) on a circle of reference is SHM. Let the particle go from P to Q in time t. Then ∠POQ=ωt=∠OQP. The projection of radius OQ on the x-axis will be OR=x(t) say.
image

 In the given triangle △OQR, sin⁡ωt=x(t)B or, x(t)=Bsin⁡ωt=Bsin⁡2πtT=Bsin⁡2πt30

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