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# Resonant Pendulum

Science Snack
Resonant Pendulum
Big swings from little pulls grow.
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.

Tools and Materials
• Empty one-gallon (3.8-liter) metal paint can with lid (a steel bucket will work, but it may spill); an unopened can of paint will work as well
• Sand to fill the paint can or bucket
• Ceramic magnet
• Several feet (3 meters or more) of string
• Length of chain or rope (shorter than room height)
• Way to suspend the can using the chain or rope
• Optional: A second magnet on a string and a partner
Assembly
1. Fill the empty paint can with sand and close the lid to prevent spills.
2. Suspend the sand-filled can from the ceiling, a tall ladder or a strong tree branch, using the chain or rope. The can should hang somewhere between waist height and ground level. (If you hang the can closer to the ground, the results will be less traumatic if it should somehow fall.)
3. Tie the magnet to a length of string.
To Do and Notice

Standing a few feet away, throw the magnet at the can while holding on to the string. 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.

If you have a 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 the two of you pull out of phase with each other, you can make the pendulum move in a circle.

What's Going On?

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).