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

Options

A. `x(t)=Bsin((2pit)/(30))`
B. `x(t)=Bcos((pit)/(15))`
C. `x(t)=Bsin((pit)/(15)+(pi)/(2))`
D. `x(t)=Bcos((pit)/(15)+(pi)/(2))`

Explanation

Let angular velocity of the particle executing motion is `omega` and when it is at Q makeks and angle 0 as shown in the diagram.
Clearly, `0=omegat`
Now, we can write `OR=OQcos(90-0)`
`=OQsin0=OQsinomegat`
`=rsinomegat` `[:'OQ=r]`
`rArrx=rsinomegat=Bsinomegat` `[:'r=B]`
`Bsin.(2pi)/(T)t=Bsin((2pi)/(30)t)`
Clearly, this equation represents SHM.