Physics

Problem

The potential energy of a particle moving along the

x

-axis is defined by

V(x)=\begin{cases} \dfrac12 kx^{2}, & x<0,\\ \dfrac12 k\,(x-0.20)^{2}+\dfrac12 k\,(0.20)^{2}, & x\ge 0, \end{cases}

where

k

is a positive constant (SI units). a. (i) Write expressions for the force

F(x)

in the regions

x<0

and

x\ge 0

. b. (ii) Identify all equilibrium position(s) of the particle and state which of them is stable.