# Resonant Frequency: Springs and Electromagnets

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### The Idea

On one side of the room, you have a bar magnet suspended from a spring. The magnet is surrounded by an electrical coil, which is attached to another coil on the other side of the room. An identical magnet is placed inside the second coil. As the first coil starts moving, an electrical current is produced, which also causes the second magnet to start moving. This is impressive to see and demonstrates several principles of physics, including resonance, magnetic induction, and magnetic force.

### What You Need

• 2 bar magnets
• 2 equal springs
• 2 wire coils with an interior opening just large enough for the magnets (these can be made or are available from scientific equipment supply companies)
• 2 ring stands with clamps to support a horizontal connecting bar; 2 pendulum clamps would be perfect
• string
• table
• connecting wire
• optional: 4 LEDs

### Method

Overall, you are going to set up two identical parts of the apparatus, shown in Figure 71-1, connected together electrically. To do this, follow these steps:

1. Suspend each of the two springs to the supports.
2. Attach the two bar magnets to the bottom of the springs using string or wire.
3. Position the bar magnets, so when the spring is displaced downward, the magnet extends into the coil, but it does not touch the table the coils are sitting on.
5. Displace one spring to set it oscillating, but leave the other spring hanging undisturbed. Observe the result.

### Expected Results

Initially, the first magnet, after being set in motion, goes up and down by itself. The motion of the first magnet generates an electrical current that causes the second magnet/spring combination to start to oscillate.

### Why It Works

The first magnet moving through the coil generates a current. This current is transmitted to the second coil. The current flowing in the second coil exerts a force on the second magnet, which sets it in motion. Because both springs are a matched set with nearly identical spring constants, the frequency of the electrical signal driving the second spring is at its resonant frequency. A small driving force at the resonant frequency has a much greater impact than a force at any other frequency.

### Other Things to Try

If you want to push your luck, you can put an LED in the electrical circuit. LEDs conduct current in only one direction. A pair of LEDs, each oriented in the opposite direction and connected in parallel, would be needed to prevent blocking the current flow. You can also put a galvanometer or a current sensor in series with one of the wires and measure the current flow directly.

Another simple way to show oscillation between magnets is to suspend two magnets horizontally from springs. Start with the north pole of one magnet facing the south pole of the other magnet. Then, turn each of the magnets from that equilibrium line. They can be turned through an angle in the same or opposing directions. The magnets will move to bring themselves back to that equilibrium position. But they will overshoot and keep going until their energy is lost to friction. Until then, they form a simple harmonic oscillator. Try this with different starting angles.

### The Point

A magnet moving in a coil of wire generates an electrical current.

An electrical current moving in a wire exerts a force on a magnet.

A simple harmonic oscillator (in this case, the spring) resonates if driven at its resonant frequency.