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)

$4\sqrt{2}$

$x=4(\cos \pi t+\sin \pi t)$
$=4\sqrt{2}(\cos \pi t\sin \pi /4+\sin \pi t\cos \pi /4)$
$=4\sqrt{2}\sin (\pi t+\frac{\pi }{4})$
So, amplitude $=4\sqrt{2}$