Question

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

Answer 1

Answer: (C)

$4 \sqrt{2}$

Answer 2

Given ,$x = 4 (\cos \,\pi t + \sin \, \pi t)$
$= 4\sqrt{2}\left(\sin \frac{\pi}{4} \cos \pi t +\cos \frac{\pi}{4} \sin \pi t\right)$
$= 4\sqrt{2} \sin\left(\pi t + \frac{\pi}{4}\right)$
Hence, amplitude = $4 \sqrt{2}$