Q. 14.11 Figures 14.25 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.

Answers (1)
S Sayak

(a) Let the required function be x(t)=asin(\pm \omega t+\phi ) 

Amplitude = 3 cm = 0.03 m

T = 2 s

\\\omega =\frac{2\pi }{T}\\ \omega =\pi rad\ s

Since initial position x(t) = 0, \phi =0

As the sense of revolution is clock wise

\\x(t)=0.03sin(-\omega t)\\ x(t)=-0.03sin(\pi t)

Here x is in metres and t is in seconds.

(b)Let the required function be x(t)=asin(\pm \omega t+\phi ) 

Amplitude = 2 m

T = 4 s

\\\omega =\frac{2\pi }{T}\\ \omega =\frac{\pi }{2} rad\ s

Since initial position x(t) = -A, \phi =\frac{3\pi }{2}

As the sense of revolution is anti-clock wise

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

Here x is in metres and t is in seconds.

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