Q. The displacement of two identical particle executing SHM are represented by equations $x_{1} = 8\ sin(10t + \pi/6)$ and $x_{2} = 5\sin{\omega t.}$ For what value of $\omega$ energy of both the particle is same?
A) 4 units
B) 8 units
C) 16 units
D) 20 units
Explanation
(c) $E = \frac{1}{2}m\omega^{2}r^{2}\ \ ie,\ \ \ E \propto (\omega r)^{2}$
or $\left( \omega_{1}r_{1} \right)^{2} = \left( \omega_{2}r_{2} \right)^{2}\ \ \ or\ \ \ \omega_{1}r_{1} = \omega_{2}r_{2}$
or $10 \times 8 = \omega \times 5\ \ or\ \ \ \omega = 16\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.