One-dimensional particle motion with potential X.

[araven7]

Homework Statement

Find the one-dimensional particle motion in the trigonometric potential
U(x) = V tan^2(a x) , V > 0 .

Find the one-dimensional particle motion in the Morse potential
U(x) = A(1-e^-ax)^2.

Homework Equations

well at the moment in class our lecturer derived: T = sqrt(2m) integral(dx / sqrt[E - U(x)]) with limits x1 and x2, where the limits of integration are the limits of the motion (or turning points), given by v=0.

The Attempt at a Solution

Im unsure as always as to what the answer should even look like. Well i started with lagrangian
L = V-U , L = m/2 v^2 - Vtan^2(ax)
and got to d/dt(dL/dv) = dL/dx, but it didnt look right and how I am unsure even how to approach the problem.

 

[Redbelly98]

Welcome to PF.

It's not clear just what is being asked. Do they simply want the period, which you can get from your equation for T?

Or do the want an expression for x(t)? For that, you would need the initial position and velocity of the particle, and to solve an integral along the lines of the expression for T.