Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated in the · figure. The simple harmonic motion of the X-projection of the radius vector of the rotating particle Pis

Options

A. `x = 2 cos (2pit +(pi)/(4))`
B. `x = 2sin(2pit +(pi)/(4))`
C. `x = 2sin(2pit - (pi)/(4))`
D. `x = 2cos(2pit -(pi)/(4))`

Answer

A

Explanation

Here = 1s
At t = 0 , OP makes an angle of `(pi)/(4) ( = 45^(@))` with the x - axis .
After time t , it covers an angle of `(2pi)/(T)t` in the anticlockwise direction and makes an angle of `((2pi)/(T) t +(pi)/(4))` with the x - axis .

The projection of OP on the X-axis at any time t is given by
` x = 2 cos ((2pi)/(T)t + (pi)/(4))`
For T = 1
`therefore X= 2 cos (2pit + (pi)/(4))`