Q. The displacement of a particle is given by $x = 3\sin{(5\pi t) + 4\cos{(5\pi t)}}$ The amplitude of the particle is
A) 3
B) 4
C) 5
D) 7
Explanation
(c) For the given super imposing waves
$a_{1} = 3,\ a_{2} = 4$ and phase difference $\phi = \frac{\pi}{2}$
$\Rightarrow A = \sqrt{a_{1}^{2} + a_{2}^{2} + 2a_{1}a_{2}\cos{\pi/2}} = \sqrt{(3)^{2} + (4)^{4}} = 5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.