Q. A particle is having kinetic energy 1/3 of the maximum value at a distance of 4 cm from the mean position, Find the amplitude of motion.
A) $2\sqrt{6\ cm\ }$
B) $2/\sqrt{6\ cm\ }$
C) $\sqrt{2\ cm\ }$
D) $6\sqrt{2\ cm\ }$
Explanation
(a) $\frac{1}{2}m\omega^{2}\left( r^{2} - y^{2} \right) = \frac{1}{3} \times \frac{1}{2}m\omega^{2}r^{2}$
or $r^{2} - y^{2} = \frac{1}{3}r^{2}$
or $3r^{2} - 3y^{2} = r^{2}$
or $2r^{2} - 3y^{2} = 0$
or $r = \sqrt{\frac{3}{2}} \times y = \sqrt{\frac{3}{2}} \times 4 = 2\sqrt{6}\ cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.