I'm a new rider who experienced an episode of severe front end shimmy while descending a fairly steep hill at roughly 40mph. I asked a physicist friend to explain what had happened (there is nothing wrong with the wheel). Here is his response:

Every mechanical system has natural modes of oscillation. Easy examples
to see are guitar strings, springs, suspension bridges... Some
mechanical systems are stiffer than others, so it might be difficult to
set a system oscillating, and see the vibrations, but they are there.
The frequency of natural vibration may be very high if the system is
very stiff, or low if it is soft. Think of a spring. The amplitudes of
the vibrations can also be big or difficult to see, depending on whether
the system is stiff or not.

When there is a force applied to the mechanical system, if the force is
applied with the same frequency as the natural frequency of the system,
you will have a "resonance." Examples of resonance are a wave in a
bathtub, if you move your hand back and forth at just the right times
you can get the wave to grow. This is a resonance. Another example,
next time you're in a shower stall, hum a note and slide the pitch up or
down until the sound reverberates and gets louder. You'll find a few
notes where the sound gets very loud, but at a slightly lower or higher
pitch you get no amplification. This is a resonance of the sound waves
bouncing off the walls of the shower stall.


Even a steady force can have a part which will drive the resonant
frequency of a mechanical system. An example of this would be wind on a
bridge, which can be steady and doesn't have to be at exactly the right
frequency to make the oscillations grow. (The key in bridge design is
to make it stiff enough that the vibrations can't grow unless the force
is extremely high.)

The front end of a bicycle is certainly a mechanical system, so will
have modes of oscillation too. It isn't very stiff, as things go, so it
is possible to excite vibrations that can grow if the force is high
enough. The force you're applying is through the brake pads to the
contact point of the tire on the road. Your weight pushing forward
because of your inertia, is pushing on the fork. All of these things
combined serve to excite the normal vibrational frequency of the
wheel/fork/frame mechanical system of your bicycle. It can be a truly
dangerous situation!

To stay away from this critical area, reduce the driving force. You do
this by a) not going so fast, b) apply as much brake-power as possible
to the rear wheels, this tends to stretch rather than compress the
frame, and also the rear fork is substantially more rigid than the front
one, c) reduce the pressure on the front brake pads if you have the
distance to roll.

Hope this helps.

Jose