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  • Figures 14.25 correspond to two circular motions.The radius of the circle, the period of revolution, the initial position,

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)

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(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 clockwise

\\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-clockwise

\\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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