# Equation for displacement in damped harmonic motion.

1. Feb 2, 2013

### Craptola

This is not really a homework problem but rather a question about an equation for displacement in damped harmonic oscillations that I've come across during revision for midterms. In my notes and in various textbooks the equation is given as $$x=C\mathrm{exp}(-\frac{b}{2m}t)\cdot\mathrm{exp}(\pm \sqrt{\frac{b^{2}}{2m}-\frac{k}{m}}t)$$

I've been told that C is a constant depending on the initial conditions of the system, but I'm not sure how to go about determining the value of this constant.
Any help on this matter would be greatly appreciated.

2. Feb 2, 2013

### Simon Bridge

You use a value for x that you know for some value of t. Usually $t=0$ and $x=x_0$ - you know, how far you pulled the pendulum back before you let it go?
You put the numbers into the equation and solve for C. It's a constant of integration.