# There are two bodies colliding Simulate the collision phenomena by num

1. Oct 28, 2011

### max1546

1. The problem statement, all variables and given/known data
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 [Broken]

2. Relevant 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)

3. 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.

Last edited by a moderator: May 5, 2017