Natural oscillation period for elastic spring

[MaxManus]

Homework Statement

I have a linear elastic spring with spring constant E, The spring is mass less, and is held fixed at the left terminal and has a mass m attached on the right terminal. We can neglict gravitational forces.

Find the natural oscillation when the tension sigma = E*epsilon, where epsilon is the strain.

The Attempt at a Solution

The one dimensional strain tensor is epsilon = du/dx
The one dimensional equation of motion for elastic media =
$$\frac{\partial^2 u}{\partial t^2} = (\frac{\lambda + 2\mu}{\rho})\frac{\partial^2 u}{\partial x^2}$$, am I supposed to use this equation?

$$\sigma = E\epsilon$$
$$\sigma = E\frac{\partial u}{\partial x}$$

Homework Statement

Homework Equations

The Attempt at a Solution

 

[MaxManus]

Anyone? I don't know which equations I should use so any help would help. F.ex this is a transverse wave?