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A ball tied to the end of a string of length 10cm is rotated with constant speed of 2m/s in a circle about the origin. Find the equation of projection of the ball on the x-axis. At t=0, the ball makes an angle of 45° with the x-axis & is travelling in anticlockwise direction.

A ball tied to the end of a string of length 10cm is rotated with constant speed of 2m/s in a circle about the origin. Find the equation of projection of the ball on the x-axis. At t=0, the ball makes an angle of 45° with the x-axis & is travelling in anticlockwise direction. Correct Answer 0.1sin(20t + 3π/4)

Let the equation of motion be: x = A sin(wt + a). The amplitude is 0.1m, w = 2/0.1 = 20s-1. a will be either π/4 or 3π/4 since at t=0, x = A/√2. The ball is travelling in anticlockwise direction so its velocity of projection at t=0 should be towards the origin and therefore negative. v = Aw cos(wt + a). At t=0, v is negative, so a will be 3π/4. Therefore eqn is: x = 0.1sin(20t + 3π/4)

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