# Damped oscillator

Sojourner01

## Homework Statement

Show that the area in phase space of a cluster of orbits for the damped simple harmonic oscillator given in the lecture varies in time as:
$$A(t) = A(0) e^{(-r/m)t}$$

## Homework Equations

$$\dot{x} = (1/m) y$$
$$\dot{y} = -kx - (r/m) y$$

## The Attempt at a Solution

I don't understand the question. I don't see how an orbit - which is a line - can have an area. I'm guessing that the result is found by some integration of the given equations, but since I don't see how the statement of the question makes any sense, I can't follow the logic.

Edit: bah. Copied down the wrong equation. The correct one is now quoted. Still, knowing the right one isn't enlightening me on what to do.

Last edited: