There are two bodies colliding Simulate the collision phenomena by num

[max1546]

Homework Statement

There are two bodies colliding
Simulate the collision phenomena by numerical integration.
(1) Confirm that the total kinetic energy is conserved if you ignore the damping forces.
(2) Show that the total kinetic energy is reduced through collision if there exists any damping.
http://img208.imageshack.us/img208/6222/springzj.jpg

Homework Equations

mx''(t)+kx(t) = 0
x''(t) + (w_n)^2 x(t) = 0
x(t) = A_1 e^(l w_n t) + A_2 e^(-l w_n t)

The Attempt at a Solution

I assumed that the second mass does not have any spring and infinite mass(wall)
Then used Runge Kutta through Matlab
===========
function Y=Func(X)
% X=(x,y), Y=(Dx,Dy)

m = 100;
k = 20;
c = 10;

x=X(1);
y=X(2);


Dx = y;
Dy = (- k* x - c* y)/m ;

Y=[Dx, Dy];

end
========
I am not sure how to arrange differential equations for this problem case in general.

 

[member 553083]

Also, I am not sure how to prove the conservation of kinetic energy and the reduction of it.Any help will be appreciated.