When the losses are small,
the solution to this equation is a sinusoid slowly decreasing with time.
Play with the simulation,
change the value of the damping factor (viscosity) and look the results.
- NOTES: remember that when introducing a new
value for the damping factor, this value is accepted only when you
the return key. When changing this factor (viscosity) take into account
that it is set on a per time-step basis (changing the time step of the
simulation would change the velocity loss factor). To restart the
from the begining, just reload it.
The frequency of the oscillations
is, for the undamped system is:
and so, the period, T = 2p/w
0 , increases with m and decreases with k. This frequency is the
we have called "natural frequency" of the system. The oscillation
slightly changes from the value reported when the system is lossy.
The effect of the friction,
represented by a non zero value of g, is to produce a gradual loss of
of the vibrating system, usually in the form of heat. If you have a
to the system when enough time has passed, the oscillations will be
and the mass will eventually be at rest. To keep the system vibrating
external force should be applied to it in order to overcome the loss of
energy due to friction. Then we can find a resonant behavior.