Question

The following figure depicts a circular motion. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated in the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P can be shown as 

• A. \(x(t)=a\cos\!\left(\dfrac{2\pi t}{4}+\dfrac{\pi}{4}\right)\)
• B. \(x(t)=a\cos\!\left(\dfrac{\pi t}{4}+\dfrac{\pi}{4}\right)\)
• C. \(x(t)=a\sin\!\left(\dfrac{2\pi t}{4}+\dfrac{\pi}{4}\right)\)
• D. x(t)=acos((π t)/(3)+(π)/(2))

Hint:

Projection of uniform circular motion on a diameter is SHM.

Answer 1

The Correct Option is A

Step 1: Angular frequency ω=(2π)/(T)=(2π)/(4)=(π)/(2)
Step 2: Initial phase from figure φ=(π)/(4)
Step 3: Equation of SHM x(t)=acos(ω t+φ)