When the applied frequency generated by an outside source matches the natural frequency of a vibrating system, resonance occurs. Resonance states are not limited to interference conditions. For example, pendulums have a natural period of
where

L represents the pendulum's length and

g represents the gravitational field strength, or the local acceleration due to gravity which is commonly taken as 9.8 m/sec^{2}.
Let's consider a pendulum having a length 1 meter. Its period would be equal to
approximately 2 seconds. Therefore it has a natural frequency of
approximately f = ½ = 0.5 hertz. If you were pushing a small child on a swing that was 1 meter long, you could push him once during each swing, that is once each 2 seconds; or you could push every other swing, once each 4 seconds; or push every third swing, once each 6 seconds. Expressing these time intervals in terms of frequency, you could push at the following frequencies: f = 1/2 = 0.50 hertz f = 1/4 = 0.25 hertz f = 1/6 = 0.17 hertz
That is, you can "drive" the pendulum's motion by applying an external forced vibration that either matches the pendulum's natural frequency or equals a submultiple of its natural frequency. In any of these instances, you could witness the swing's resonance by noticing its amplitude increasing with each push.
