Question

Figures 14.29 correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure.

Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.

Answer 1

(a) Time period, T = 2 s

Amplitude, A = 3 cm

At time, t = 0, the radius vector OP makes an angle with the positive x-axis, i.e., phase angle

Therefore, the equation of simple harmonic motion for the x-projection of OP, at time t, is given by the displacement equation:

(b) Time period, T = 4 s

Amplitude, a = 2 m

At time t = 0, OP makes an angle π with the x-axis, in the anticlockwise direction. Hence, phase angle, Φ = + π

Therefore, the equation of simple harmonic motion for the x-projection of OP, at time t, is given as: