Resonant Pendulum
Big swings from little pulls grow.
By exerting very small forces at just the right times, you can make a massive pendulum swing back and forth in very large swings.

• A metal paint can (1 gallon [3.81] size with lid). A sand-filled steel bucket will work, but the sand may spill.
• A large hook or eye bolt to attach the chain or rope securely to the ceiling.
• Sand to fill the paint can.
• A ceramic magnet on a few feet of string.
• Optional: A second magnet on a string.

(15 minutes or less)

Fill the paint can with sand, close the lid to prevent spills, and suspend it from the ceiling with the chain or rope. The can should hang somewhere between waist height and ground level. The closer to the ground it hangs, the less traumatic the results if it should somehow fall.

(15 minutes or more)

Stand a few feet away and throw the magnet at the can. Your goal is to get the magnet to stick to the can. Once you have done this, pull gently on the string to set the can in motion. If you pull too hard and the magnet pulls off, try again. By pulling very gently on the string, but only pulling when the pendulum is moving toward you, you can gradually make the pendulum swing in very large swings.

By using the second magnet on a string, a second person standing 90 degrees to the side of you can make the pendulum move along a diagonal line between the two of you by pulling gently at the same time that you do. If they pull out of phase with you, they can make the pendulum move in a circle.

A very small force, when applied repeatedly at just the right time, can induce a very large motion. This process 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 10 times. Then divide this time by 10. You now have the period of one 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 10 swings take 20 seconds, then the period is 2 seconds. The frequency is 1 divided by 2 seconds, or one-half of a cycle per second (one-half hertz, or l/2 Hz).

This device can double as a dramatic potential-to-kinetic-to-potential energy demonstration. Pull the can to one side until it just reaches your nose. (Adjust the length of the rope as necessary to allow this.) Let go of the can (without pushing!) and stand very still (without moving your head forward!), and the pendulum will return repeatedly without striking your face. A bowling ball with a large eyebolt screwed into a predrilled hole can be substituted for the paint can in this demonstration, since no magnet is used and, hence, a metal can is not necessary. The paint can or bowling ball will not hit you in the nose, because of the law of conservation of energy. To swing farther, the pendulum must rise higher; to rise higher, it needs more energy. If no energy is added during the swing, the pendulum cannot hit you in the nose.