Harmonic Pendulum

The overall goal of this system is to generate a melody using pendulums, creating a connection between physics, electronics, computer science, and music. The project combines a custom-built 12-note copper pipe metallophone (xylophone) with an automated electronic system triggered by the physical oscillation of harmonic pendulums.

Xylophone Materials:

- 12 Copper Pipes (precisely cut for the notes)

- Wooden Structure & Base Support

- 48 Nails (used as alignment guides)

- Elastic Bands

Pendulum & Electronics Materials:

- 12 50g metal balls with a hook

- 0.5 mm / 100 m Transparent nylon monofilament fishing line

- 7 wooden slats & 6 bolts

- 12 Lasers & 12 3D printed laser supports

- 12 Photodiodes & 12 100 kΩ resistors

- 12 Mini DC motors & 12 buttons (with 3D printed supports)

- 12 Linear Solenoids

- 3 Relay modules (4-relay type)

- Arduino board & 1000 Ω resistors

- Copper tape, superglue, hot glue, solder, and tin

- Two 5V power supplies

The project began with a phase of both acoustic and computational research. To select the ideal frequencies, we developed a custom program designed to analyze harmonic relationships and determine which notes complemented each other best. Using this software, we defined a 12-note scale focused on high frequencies: G8, F8, D8, C8, A7, G7, F7, D7, C7, A6, G6, and F6.

Building the Xylophone:

1. Cutting the Pipes: Cut the copper pipes into precise lengths to match these specific pitches.

2. Calculating Nodes: Accurately calculate the position of the nodes and antinodes for each pipe to identify the optimal support points, preventing any dampening of the metal's natural vibration.

3. Frame Assembly: Build the custom wooden structure, adding a support to the base to increase stability, and paint the entire frame a vibrant fuchsia.

4. Securing the Pipes: Align the pipes, position 4 nails around each one to act as containment guides, and apply elastic bands to lock them safely in place.

Next, we assemble the physical harmonic pendulum structure.

Instructions:

1. Main Plank: Take a wooden slat 72 cm long, screw on the screw hooks 8 cm apart, and drill very small holes 6 cm from each hook.

2. Rigging the Balls: Cut the fishing line to the desired length to reach your planned pendulum frequency. Insert the 50g metal ball into the wire.

3. Securing the Lines: Tie one end of the line to the hook and apply hot glue to secure it. Pass the other end through the drilled hole and glue it with superglue to the mini DC motor. Repeat this process for all 12 balls.

4. A-Frame Supports: Create 2 equilateral triangles with the remaining pieces of wood, secure them with bolts, and attach the main 72 cm slat to these supports.

The electronic system consists of four main interconnected circuits. Refer to the provided schematic drawings for accurate pin matching.

1. Laser Circuit

Place 12 lasers in a row beneath the pendulum plank. Connect each laser to the power supply (5V or less) through a 1000 Ω, with the other terminal connected to GND.

2. Photodiode Circuit

Implement 12 photodiodes in a row on the lower plank, aligned perfectly with the lasers. Wire each photodiode in parallel with a 100 𝑘Ω resistor. Connect one terminal to GND and the other to an analog pin of the Arduino (A0–A11).

3. Solenoids & Relay Circuit

Arrange 12 solenoids beneath the xylophone tubes. Connect each solenoid to a dedicated 5V power supply and a relay output on the 4-relay modules (3 modules in total, sharing a common GND with the Arduino).

4. DC Motors Reel Circuit

Mount the 12 DC motors on the pendulum plank. Weld each motor to its respective 6-terminal switch button. Connect the switches to GND and an independent power supply (under 5V is recommended for smoother line adjustments). This setup allows you to wind or unwind the line to adjust the pendulum lengths manually.

The automated logic is handled entirely by the Arduino code, working as follows:

1. Continuous Scanning: The system starts by continuously monitoring the analog signals from the 12 photodiodes.

2. Laser Alignment: Each laser points precisely at its corresponding photodiode to maximize the base light intensity reading.

3. Interruption/Trigger: When a pendulum mass swings past its resting center point, it temporarily obstructs the laser beam. This cause a sudden drop in light intensity detected by the photodiode.

4. Sound Generation: The Arduino detects this significant signal drop and immediately triggers the respective relay control circuit. The chosen relay closes, powering the solenoid which strikes the copper pipe directly above it, producing a crisp, mathematically synchronized note.