A very small force, when applied repeatedly at just the right time, can induce a very large motion. This phenomenon is known as resonance. Perhaps the most familiar example of resonance in everyday life is swinging on a playground swing. The first push or pump sets the swing in motion. Each subsequent push or pump is delivered at just the right time to increase the amplitude of swing. If you continue pushing or pumping over a period of time, the swing will gradually go higher and higher.
Every pendulum, from a playground swing to your hanging paint can, has a frequency at which it tends to swing. This is the pendulum’s natural frequency. To find the natural frequency of a pendulum, just pull it to the side and release it. The pendulum will swing back and forth at its natural frequency. If the frequency of pushes on a pendulum is close to the pendulum’s natural frequency, the motion and the pushes will remain in step. Each successive push will increase the amplitude of the motion of the object.
You can measure your pendulum’s natural frequency using a stopwatch or a timer. Time how long it takes the pendulum to swing back and forth ten times. Then divide this time by ten. You now have the period of one back-and-forth swing of the pendulum. The frequency is the inverse of the period. To get the frequency, just divide one by the period. For example, if ten swings take twenty seconds, then the period is two seconds. That means the frequency is 1 divided by 2, or one-half of a cycle per second (one-half hertz, or 0.5 Hz).