Galileo noted that the swings of a pendulum increasingly grow with repeated timed
applications of a small force. This phenomenon is called resonance and it
occurs when the frequency of an applied force matches the natural frequency of a
system. Large-amplitude oscillations are the results of resonance.
Let's take a spring system for example.
Suppose that this force is applied at all times, not just for a brief initial moment.
This additional force is known as the driving force . When the driving force
has the same frequency as the spring system and always points in the direction of the
objects's velocity, a great increase in the amplitude of the vibration occurs.
The natural frequency of a spring system is shown below.
Resonance explains why a swaybridge (Like the Tacoma's narrows bridge) collapsed
in a mild wind and how a wineglass can be shattered to pieces by a human voice.