# Determine the oscillation period

1. Mar 7, 2014

1. The problem statement, all variables and given/known data

Determine the oscillation period, as a function of energy E, when a particle of mass m moves in a field with potential energy $V(x)=-V_0/cosh^2(\alpha x)$, for $-V_0 < E < 0$ with Vo positive.

(a) First show that, with s=sinh (α x) and determining the appropriate smax ,the period satisfies

$T=\frac{2\sqrt{2m}}{\alpha\sqrt{E}}\int_{0}^{S_{max}}\frac{ds}{\sqrt{s^2}+\frac{E+U_o}{E}}$

2. Relevant equations
Not sure where to start. My text-book is of no help when it comes to this question

3. The attempt at a solution
I am not sure where to start....

Can someone help me with this one. thanks!

2. Mar 7, 2014

### TSny

Show some attempt. You know you need to use energy ideas. What can you say about the relation between kinetic energy, potential energy, and total energy E?

3. Mar 7, 2014

T + v = e.... Don't see what the would do?

4. Mar 7, 2014

### TSny

Suppose you could express the speed v as a function of x. Note v = dx/dt. So, you would have dx/dt = some function of x.

5. Mar 7, 2014

Ya I get that, i just don't know how to get smax

6. Mar 7, 2014

### TSny

What can you say about the value of the potential energy V(x) when s = smax?