Question

A particle oscillates in a plane as per the relation $x=4\left(cos\right(\pi t)+sin(\pi t\left)\right)$. Find amplitude of oscillations.

Answer 1

REF.Image.

Displacement of particle:-

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

In superposition of oscillation in perpendicular phases,

so resultant,

$R^2=4^2+4^2$ (by phases addition)

$\Rightarrow R=4\sqrt{2}$ (Ans)