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Q. 14.12 (a) 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(3t+\pi /3)

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\\x=-2\sin(3t+\pi /3)\\ x=2cos(3t+\frac{\pi }{3}+\frac{\pi }{2})\\ x=2cos(3t+\frac{5\pi }{6})

The initial position of the particle is x(0)

\\x(0)=2cos(0+\frac{5\pi }{6})\\ x(0)=2cos(\frac{5\pi }{6})\\ x(0)=-\sqrt{3}cm

The radius of the circle i.e. the amplitude is 2 cm

The angular speed of the rotating particle is \omega =3rad\ s^{-1}

Initial phase is 

\\\phi =\frac{5\pi }{6}\\ \phi =150^{o}

The reference circle for the given simple Harmonic motion is

Reference plot for SHM

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