The time-step you use will determine the accuracy of the system you are trying
to simulate. If it is too long, you will be missing some of the 'detail' in the
simulation, this can result in instability in the simulation. On the other hand,
if it is too short you will waste processing time unnecessarily.

The instability can be caused by a long time-step introducing an error in your
calculations, which builds up over succesive time-steps, becoming ever larger.
Ultimately you will have to find a time step that will produce an acceptably low
error (and hence reduce or eliminate instability) over the full length of the
simulation.

You should also note that some simulations produce stable oscillations in the
system which don't ever dissipate. This will be because the system you are
simulating would in real life oscillate in this way. If increasing the time-step
does not remove all oscillation then you can assume they are there to stay.

The rate of change of the forces on the particles will determine the time-step
you need. If the forces change rapidly then your system will require a very
short time-step to correctly simulate the motion of the particle under those
conditions. Otherwise a longer time-step will not properly account for those
changes in force.

For example:
If you were to apply an oscillatory acceleration of the form:
acc=A*cos(2*pi*t)
If you sample the acceleration every 1 second, your simulation will see a
constant acceleration of magnitude A for the entire duration of the simulation
(resulting in particles that start moving and just get faster and faster). This
is obviously not the kind of behaviour that an oscillatory acceleration should
produce, and is a result of the sample rate being too long.

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