Question

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

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

Answer 1

Correct Answer - A

Here, T=30s
At t=0, OP makes an angle of `(pi)/(2)` with the x-axis
After a time t, it covers an angle
of `(2pi)/(T)t` in the clockwise
sence, and makes an angle of
`((pi)/(2)-(2pi)/(T)t)` with the x-axis
the projection of OP on the x-axis at time t is given by
`x(t)=Bcos((pi)/(2)-(2pi)/(T)t)=Bsin((2pi)/(T)t)`
`x(t)=Bsin((2pi)/(30)t)" "(becauseT=30s)`