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)

$4\sqrt{2}$

The displacement equation is given as: $x=4(cos\pi t+sin\pi t)$

$x=4\sqrt{2}$ $(\frac{1}{\sqrt{2}}cos\pi t+\frac{1}{\sqrt{2}}sin\pi t)$

$x=4\sqrt{2}$ $(sin{45}^{o}cos\pi t+cos{45}^{o}sin\pi t)$

$x=4\sqrt{2}$ $sin(\pi t+{45}^o)$

Comparing with, $x=A$ $sin(wt+\varphi )$

$⟹$ Amplitude of the particle, $A=4\sqrt{2}$