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Figure shows the circular motion of a pa...


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

A

`x=2cos(2pit+(pi)/(4))`

B

`x=2sin(2pit+(pi)/(4))`

C

`x=2sin(2pit-(pi)/(4))`

D

`x=2cos(2pit-(pi)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, `T=1s`

At t=0, OP makes an `(pi)/(4)(=45^(@))` with the x-axis
after a time, it covers an angle of `(2pi)/(T)t` in the anticlockwise sense and makes an angle of `((2pi)/(T)t+(pi)/(4))`
with the x-axis
The projection of OP on the x-axis at time t is given by
`x=2cos((2pi)/(T)t+(pi)/(4))`
For, T=1s
`thereforex=2cos(2pit+(pi)/(4))`
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