# Solve the equation for the harmonic oscillator given initial conditions

• Aug 3rd 2014, 12:31 AM
Cotty
Solve the equation for the harmonic oscillator given initial conditions
Hi,

I have a question I have been trying to get out, and I'm not having much luck by myself. I'm sure I have solved equations like this in the past, although I cannot find my notes anywhere to help. I have attached a screenshot of the questions, but it says to solve the equation for the harmonic oscillator given the initial conditions:

$$x(0) = x_0$$
$$\frac{dx}{dt} = v_0 \quad at \quad t=0$$

Also I was assuming that this was the equation we had to work with?

$$m \frac{d^{2}x}{dt^{2}} \quad + \delta \frac{dx}{dt} \quad + kx = 0$$

Can you please point me in the right direction? Any help would be greatly appreciated!!

Attachment 31385

Thanks,
Cotty.
• Aug 3rd 2014, 01:33 AM
romsek
Re: Solve the equation for the harmonic oscillator given initial conditions
http://www.ncsu.edu/crsc/events/ugw0...t_harmonic.pdf

should have everything you need to solve this.
• Aug 3rd 2014, 02:32 AM
Cotty
Re: Solve the equation for the harmonic oscillator given initial conditions
Thanks Romsek, that looks like it will be very helpful