Question

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 simple harmonic motion of the $x$ - projection of the radius vector of the rotating particle P is:

• A. $x\left(t\right)=Bsin\left[\frac{2\pi }{30}t\right]$
• B. $x\left(t\right)=Bcos\left[\frac{2\pi }{15}t\right]$
• C. $x\left(t\right)=Bsin[\frac{\pi }{15}t+\frac{\pi }{2}]$
• D. $x\left(t\right)=Bcos[\frac{\pi }{15}t+\frac{\pi }{2}]$

Answer 1

The correct option is A $x\left(t\right)=Bsin\left[\frac{2\pi }{30}t\right]$

Given:

$w=\text{angular frequency}=\frac{2\pi }{T},T=\text{Time period}=30sec$

$x\left(t\right)=Amplitude\times \sin wt=B\sin \frac{2\pi t}{T}=B\sin \frac{2\pi t}{30}$

Option $A$ is the correct answer.