Question

The displacement of a particle varies according to the relation $x = 4(cos\, pt + sin \,pt).$ the amplitude of the particle is

• A. $-4$
• B. $4$
• C. $4v2$
• D. $8$

Answer 1

Answer: (C)

$4v2$

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 = $4 \sqrt{2}$