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Question

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


A
x(t)=B sin(2πt30)
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B
x(t)=B cos(πt15)
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C
x(t)=B sin(πt15+π2)
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D
x(t)=B cos(πt15+π2)
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Solution

The correct option is A x(t)=B sin(2πt30)
Given, T=30 s,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=OQR
The projection of radius OQ on X - axis will be OR=x(t) say.
In ΔOQR,sin ωt=x(t)B
x(t)=B sin ωt=B sin 2πTt=B sin 2π30t

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