# Resonance of a Swing at Its Natural Frequency

4.7 based on 3 ratings

### The Idea

When you push someone on a swing, timing is important. If you push just as the swing has come to its highest point and is ready to begin its return, you will keep the swing going and increase its amplitude. However, if you push randomly, your efforts will be far less effective and, at times, you will tend to slow the motion of the swing. The reason for this is a swing has a natural frequency. If your pushing is at the natural frequency of the swing, the swing will resonate. This experiment explores the idea of resonance.

### What You Need

• 2 ring stands
• 1⅜ inch diameter wooden dowel, 12 inches long
• 2 clamps (to hold the dowel)
• string of various lengths, from about 3 inches to 10 inches
• set of several small masses that can be attached to the string (large stainless steel nuts work well here or any attachable masses in the overall range from 10–50 g)

### Method

1. Tie loops at one end of each of the strings and tie the other end to a mass. At least two of the strings should be the same length. The other should be random—some larger and some smaller than the matched pair. Avoid, however, having all the other strings half or double the size of the matched pair.
2. Slide the loops onto the dowel and spread the strings out evenly across the length of the dowel. The two matched strings should not be next to each other.
3. Attach the dowel to the two upright posts of the ring stands using the clamps. Leave enough space, so all the masses are free to swing without hitting the table, which the ring stands are placed on. The dowel should be slightly flexible, but constrained by the ring stands, so it will not sway or swivel when the masses are swinging. See Figure 69-1.
4. Steady all the masses hanging on the strings.
5. Take only one of the masses on the matched strings and displace it, so it is swinging perpendicular to the direction of the dowel.

### Expected Results

What we want to see here is for the stationary string, which is the same length as the one that was set in motion, to also start moving back and forth. The other masses might jostle around a bit, but they should not be set into a significant swinging motion.

### Why It Works

The resonant frequency of a pendulum is determined exclusively by the length of the string that supports it. The stationary pendulum is stimulated by the swinging pendulum that has the same length and, therefore, the same natural frequency.

### Other Things to Try

Other questions that can be addressed are:

1. Would a pendulum with the same string length, but different mass, have the same resonant frequency as the swinging pendulum?
2. What if we throw in a few harmonics? What is the response of a pendulum that is one-half the length of the swinging pendulum? What is the response of a pendulum that is double the length of the swinging pendulum?

### The Point

A simple harmonic oscillator, such as a swinging (simple) pendulum, has a natural frequency. If stimulated at that natural frequency, the amplitude of that pendulum will be greatest.