In 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

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))`

Answer

A

Explanation

Let angular velocity of the particle executing circular motion is `omega` and when it is at Q makes and angle `theta` as shown in the diagram.

Clearly, `theta=omegat`
Now, we can write `OR=OQ cos (90-theta)`
`=OQ sin theta=OQ sin omegat`
`=rsinomegat" "[because OQ=r]`
`x=rsinomegat=Bsinomegat" "[because r=B]`
`=B"sin"(2pi)/(T)t=B"sin"((2pi)/(30)t)`
Clearly, this equation represents SHM.