# Homework Help: Trace-determinant plane: underdamped systems

1. Dec 8, 2009

### clarineterr

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

Describe the set of points on the trace-determinant plane that describe all underdamped systems with period 2

2. Relevant equations

A harmonic oscillator can be represented by the equation m$$\frac{d^{2}y}{dt^{2}}$$ +b$$\frac{dy}{dt}$$+ky=0 the Trace=-b/m and the Determinant=k/m.

For an underdamped oscillator, the period is 4m$$\pi$$/$$\sqrt{4km-b^{2}}$$
and T$$^{2}$$-4D

3. The attempt at a solution

I have been trying to solve the equation 4m$$\pi$$/$$\sqrt{4km-b^{2}}$$=2 and then find T and D, but no luck really. I think the answer is all the points above a certain parabola.