# 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.

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.

Exams
Articles
Questions