Proving the superposition of initial conditions gives superposition of motion

[mcah5]

I have a problem that says to prove the superposition of initial conditions gives superposition of corresponding motion for two coupled oscillators. My question is:

What do they mean by coupled oscillators? Do they mean coupled pendulums? Double LC circuits? If it's coupled pendulums are the pendulums the same mass? I know how to do the math for the specific types of coupled oscillators, but I don't think there is a general way to derive the motion of coupled oscillators without specifics about what type oscillator it is.

 

[Galileo]

You should know the differential equation governing the motion of the system.
All you really require is that the DE's be linear.

 

[mcah5]

Edit: I can't use Latex =(

Ah, thank you