Q. The displacement of a particle varies according to the relation $x = 4(\cos{\pi t + \sin{\pi t).}}$ The amplitude of the particle is
A) -4
B) 4
C) 4$\sqrt{2}$
D) 8
Explanation
(c) $x = 4(\cos{\pi t + \sin{\pi t)}}$
$= \frac{4}{\sqrt{2}} \times \sqrt{2}\left\lbrack \cos{\pi t} + \sin{\pi t} \right\rbrack$
$x = 4\sqrt{2}\sin{\lbrack\pi t + \frac{\pi}{4}}\rbrack\ $
So, amplitude=$4\sqrt{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.