### Q.12:- Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial (*t *= 0) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: (*x *is in cm and *t *is in *s*).

### (a) *x *= –2 sin (3*t *+ π/3)

(b) *x *= cos (π/6 – *t*)

(c) *x *= 3 sin (2π*t *+ π/4)

(d) *x *= 2 cos π*t*

**Answer:-**

(a)

Amplitude,

*A*= 2 cmPhase angle,

*Φ*= 5π/6 = 150°.Angular velocity = ω = 2π/

*T*= 3rad/sec.The motion of the particle can be plotted as shown in fig. 10(a).

(b)

Amplitude, A = 1

Phase angle,

*Φ*= -π/6 = -30°.Angular velocity, ω = 2π/

*T*= 1 rad/s.The motion of the particle can be plotted as shown in fig. 10(b).

(c)

Amplitude,

*A*= 3 cmPhase angle,

*Φ*= 3π/4 = 135°Angular velocity, ω = 2π/

*T*= 2 rad/s.The motion of the particle can be plotted as shown in fig. 10(c).

(d)

Amplitude,

*A*= 2 cmPhase angle,

*Φ*= 0Angular velocity, ω = π rad/s.

The motion of the particle can be plotted as shown in fig. 10(d).