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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. | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-14 Oscillations

Q.11:- 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:-**
(a) Time period, t = 2 s

Amplitude, A = 3 cm

At time, t = 0, the radius vector OP makes an angle π/2 with the positive *x*-axis,.e., phase angle *Φ* = +π/2

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