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

Answer

A

Explanation

Let angular velocity of the particle executing circular motions is `omega` and when it is `P` makes and angle `theta` as shown in the diagram.
As `sin theta = (x)/(OP) =(x)/(B)`,
Clearly, `theta = omegat`
`x = B sin thetaB(sin omegat) = B sin ((pit)/(15))`
`x = B sin ((2pi)/(30)t)`