A particle of mass m moving in one dimension is subject to the potential (x) = V₁²²2e-², a>0. a) Draw a qualitative plot of the potential function. Find the location(s) of any equilibrium positions in terms of V, and a and state whether they are stable or unstable. b) Write down the Lagrangian and the Euler-Lagrange equation.

A particle of mass m moving in one dimension is subject to the potential (x) = V₁²²2e-², a>0. a) Draw a qualitative plot of the potential function. Find the location(s) of any equilibrium positions in terms of V, and a and state whether they are stable or unstable. b) Write down the Lagrangian and the Euler-Lagrange equation.