Damped Coupled Oscillators, Deformations and Energy Lost in Collisions

[Sidnv]

I'm doing a research project on collisions and I've come across a part of my theory that requires solutions to coupled damped oscillators.

Could anyone please refer me to some text on 2 coupled damped oscillators which isn't extremely math heavy and has conceptual explanations of the solutions?

If it helps the equations of motion are probably the following

d2x1/dt^2 + Yc(dx1/dt - dx2/dt) + wc^2(x1-x2) = 0

d2x2/dt^2 + Ys(dx2/dt) + ws^2(x2) = 0.

Also, can anyone recommend me an extremely elementary level text on deformations, elastic potential energy, pressures and stress/shear that takes place during collisions of two objects.
Eg: Collision of two billiard balls, collision of two rubber balls, collision of billiard ball and floor, collision of rubber ball and floor.
In addition a text on the way in which the sound produced and the different characteristics of sound produced (energy, frequency, amplitude) during such collisions would be greatly helpful. I'm particularly focussing on the energy lost in a collision and the proportion of said energy lost through sound, heat and elastic potential energy(change in shape/structure).

I'd love it if anyone could give me direct answers to my questions but even a link to papers on the above topics would be deeply appreciated.

Thanks,
Sid

 

[marcusl]

I can address your first question. Marion, Classical Dynamics of Particles and Systems (1970) has a nice chapter on coupled oscillators. It's a standard undergrad text.

 

[Sidnv]

Thanks. I'll take a look at that.