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

The correct option is C $4\sqrt{2}$

$x=4(cos\pi t+sin\pi t)$

$cos\theta$ & $sin\theta$ both can have

maximum value simultaneously

only if $\theta ={45}^{\circ }$

$\Rightarrow x/max=4(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}})=4\sqrt{2}$