The oscillations we have discussed up to now are
free oscillations in which
the system is given some energy, then left alone.
For instance, you could pull a child on a swing up to a certain height, then
let go and wait for the motion to die away.
But this is not the only possibility; we could also repeatedly push the
swing at any frequency we like and watch what happens.
In this case we say that we have
forced oscillations.
There are now two frequencies in the problem: the natural frequency
of the free oscillations,
and the driving frequency 
of the
forced oscillations.
This means that you will have to resist the urge to use the formula 
whenever you encounter a frequency.
If the frequency in question is the driving frequency, there is no formula for it; it is
simply set by the design of the driving circuit.
Transients and Steady State: Now, how does the oscillating system respond to this oscillating driver?
The equations are too complicated to solve here, so we will use our
mechanical analogy again.
If the mass-spring system is driven at a frequency other than its
natural frequency, a rather complicated motion results.
The mass will start to oscillate, then stop, then start up again, and stop again,
over and over.
The reason for this odd motion is that there are actually two motions occuring simultaneously,
one at the natural frequency, , and one at the driving freqency, .
If we wait long enough, however, the motion at the natural frequency
will die away because of friction, leaving only the motion at the
driving frequency.
This initial period of complicated motion is called a transient, and
in this course we will ignore it.
We are only interested in the final motion at the driving
frequency, which is sometimes called the steady state motion.
Electric circuits behave in the same way.
When you plug an appliance into the wall, an oscillating emf at 60 Hz is
applied to it.
For a very brief period of time there is a complicated variation of
the current with time, but after this transient dies away, the
current in the appliance oscillates steadily at 60 Hz.