Vernier Software and Technology
Vernier Software & Technology
Innovative Uses

A Smart Wilberforce Pendulum

By Keith Clay, Green River College

A Wilberforce pendulum is a physics toy that would drive Iron Man to distraction. Simply put, it is a mass tightly attached to the end of a spring that can oscillate up and down and twist back and forth. If the vertical and twisting motions have similar frequencies, the pendulum repeatedly alternates between the two, twisting side to side and then bobbing up and down as energy is passed between vertical and rotational motion.

The pendulum stands six meters high, top to bottom.
The pendulum stands six meters high, top to bottom.

At Vernier, we recently built a Wilberforce pendulum using a Go Direct® Force and Acceleration Sensor, a Rotational Motion Accessory Kit, and a metal Slinky®. We used Graphical Analysis 4 to receive and graph data from the Go Direct Force and Acceleration Sensor. The sensor uses an internal gyro to track the rotation and uses the onboard accelerometer or force sensor to track the vertical motion. It beautifully displays the beats of an oscillator with two normal modes.

Force and rotational motion data were collected from the tabletop Wilberforce pendulum using Graphical Analysis. The exchange of energy between vertical and rotational modes of motion can be seen in the interplay of measured force and rotational velocity.
Force and rotational motion data were collected from the tabletop Wilberforce pendulum using Graphical Analysis. The exchange of energy between vertical and rotational modes of motion can be seen in the interplay of measured force and rotational velocity.

The data shown here were collected from a tabletop version made with a sensor, a lab spring, and washers, nuts and bolts to tune the inertia. We also built a pendulum six meters high using a Slinky for the spring and a Rotary Motion Accessory Kit in place of the bolts and washers.

A Wilberforce pendulum provides great opportunities for exploration. You can ask students to measure the moment of inertia or the torsional spring constant. Challenge students to name and measure five relevant forms of potential and kinetic energy. Or simply watch as it goes through its graceful dance, dutifully graphing the motion.

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