# Coupled mass spring system with damping and initial values

After researching through the web, I can't figure out how to express into a differential equation a coupled mass spring system with damping and initial values. Two masses and two springs, no external forces, just gravity because of vertical position. I know that $mx''+cx'+kx=f(t)$ is used for single spring systems, but it's useless on coupled systems. The values are:

• 1st spring: $k=3, c=1, x(0)=.1\text{ m}$ (initial position), $x'(0)=1\text{ m/s}$ (initial velocity)
• 2nd spring: $k=1, c=3, x(0)=-.1\text{ m, } x'(0)=0\text{ m/s}$

Both masses $=1$

I don't need a solution, I just need the differential equation to solve this system through Laplace transform. Hope someone can help this desperate man.

• Without telling us what the problem is or what it looks like, it's hard to give an answer. – DumpsterDoofus Mar 7 '14 at 5:22
• It looks like this upload.wikimedia.org/wikipedia/commons/f/fd/… Again, I just want to know how to place all those values in a differential equation. – user42032 Mar 7 '14 at 5:29
• You don't just place values in the differential equation...You solve the differential equation and use those values as your initial conditions (i.e. solve for integration constants). Also what is $f(t)$? Can't solve without that. I am surprised you have not received any down votes for this question. I would suggest giving SE all the information and your attempt. Lastly, is this a HW problem? – jerk_dadt Mar 7 '14 at 5:44
• Like I said in the description, if I wanna calculate an equation for a single mass spring system I would use that second order differential equation. Now, for a coupled mass spring system, which form of differential equation I have to use? f(t) is the external forces, there aren't external forces, but because the system is in vertical position, f(t)=mg. Yes, this is a HW problem. I don't have an attempt because I don't have the differential equation to start with. – user42032 Mar 7 '14 at 5:48
• In fact, this is a mathematics homework, I admit I never liked physics. Could you explain me how do I use that equation for both springs? – user42032 Mar 7 '14 at 6:15