Question

The potential energy of a particle of mass $0.5$ kg moving along x-axis is given by $U=(x^2-4x)$ joule where x is in metres. The time period of oscillation of the particle is?

Answer 1

$F=\frac{-du}{dx}=20–10x.$

Also$F=0$,inmeanposition.

So$x=2$isthemeanposition.

Foradisplacement$dx,F=F(x+dx)-F\left(x\right)=-10dx.$

Comparingwith$F=-kdx,wegetk=10.$

Also$m=0.1kg.$

Hence$T=2\pi \left(\frac{m}{k}\right)=\frac{2\pi }{10}=\frac{\pi }{5}second.$