Spring Mass Systems:  Start of Simulation

Simulate the Behavior of the System, starting from some given initial state
(initial value problem):

Conceptually it is clear what needs to be done:

-- calculate the forces resulting from the stretched/compressed springs;

-- calculate the resulting force on each mass ("particle");

-- divide by the mass of a particle to obtain its acceleration;

-- calculate an updated velocity for that particle;

-- move each particle according to its current velocity times a small time step h;

-- calculate new positions for all particles;

-- repeat the above six process steps.

This simple numerical method is called the (forward or explicit) Euler method.

It works OK for small time steps and if the system is not too stiff.

Let's look at the problems that may arise ...