- #1

Vitani11

- 275

- 3

## Homework Statement

Here is the equation for the general solution of an overdamped harmonic oscillator:

x(t) = e

^{-βt}(C

_{1}e

^{ωt}+C

_{2}e

^{-ωt})

## Homework Equations

β decay constant

C

_{1}, C

_{2}constants

ω frequency

t time

## The Attempt at a Solution

I know (e

^{ωt}+e

^{-ωt})/2 = coshωt and (e

^{ωt}-e

^{-ωt})/2 = sinhωt but how do I implement this if there are constants? I tried to solve for the constants, but I just get a nasty expression in terms of x(o) and v(0) for each C (where v is the velocity) and this doesn't help with rewriting the functions.