The vibrating systems described in this unit are "free" vibrators. The system is given some energy (for example, by displacing a pendulum), and during the vibrational motion the energy is largely constant (the pendulum will swing a long time before air resistance brings it to a halt). However, there is another kind of vibrating system, where an external force is acting. For example, the loudspeakers of a stereo only make sound when the applied electrical signal tells them to do so. The motion of the speaker cone is similar to the motion of a pendulum, in that each moves back and forth around an equilibrium position; the difference is that the force acting on the pendulum is due to its displacement, while the force acting on the speaker comes from outside the speaker itself. The result is that the speaker can vibrate at any frequency, while the frequency of the pendulum is determined by its construction.
Everyday examples of a driven oscillator are the washing machine that shakes, the refrigerator that hums, or a car that rattles as it drives over a grate or grooved pavement.
An interesting situation arises when an external vibration force is applied to a system that will also vibrate on its own. If the frequency of the applied force is close to the natural frequency of the vibrating system, the amplitude of the vibration can be come very large. The external force will be pulling on the system when it is moving one way and pushing when it is moving the other way, which causes the energy to increase. This effect is called resonance. For example marching soldiers are told to break step when they cross a bridge. The concern is that the thousands of feet all stamping at once might start a large vibrational motion of the bridge. It's actually pretty unlikely that the bridge would vibrate at the rate the soldiers are walking, or that the relatively small force they can apply would affect the bridge much, even if multiplied many times by the resonance effect; however, on a sufficiently rickety bridge this could be a useful safety measure.
Another example are the tides. The oceans are rotating with the earth, and then the gravitational force of the sun and moon are in different directions at different times of the day. The result is that there is a periodic force that causes the shape of the ocean surface to vibrate up and down twice a day. If the world were mostly ocean, the amplitude of this motion would be 54 cm, and one of the high tides would occur when the moon was most nearly overhead (moon noon!). However, there is a vibrational aspect to the way a bay fills up and empties (it's like water sloshing in a very large bathtub), and if the natural vibration period of the bay is close to a half-day, the tides can be much larger due to the resonance effect; this also shifts the timing of high tide relative to the moon-noon.