Concepts

Normal modes at resonant frequency

Overview

Two carts are connected by springs on a track. The coupled carts are then connected by a spring to one end of the track and by another spring to a driving motor that is controlled by a variac. At resonant frequency, the two carts move in opposite directions.

Details

Equipment

• [1] Variac
• [1] DC motor
• [2] Cart
• [1] Cart track
• [6] Spring
• [1] String
• [3] 250 g mass
• [4] Small magnet

Classroom Assembly

1. Place the track on a horizontal platform near a power outlet.
2. Connect a DC motor to the variac and position the motor such that students can see the rotation of the motor clearly.
3. Add as many damping magnets to the cart bottoms as desired.
4. Start with voltage at 0 V to begin.

Important Notes

• Increase the voltage carefully, and be sure not to apply a voltage larger than 100 V
• If cart oscillations are too strong, add more magnets to the undersides of the carts

Script

1. Connect the springs and the carts as shown on the image, if they are not already connected.
2. Attach the spring to a screw at the end of the track.
3. Connect the spring to a motor by a string.
4. Turn on the variac and slowly increase the voltage.
5. Put a 250 g mass on top of the cart to increase the mass of the cart if necessary. Note that the mass of the cart is approximately 250 g.

Additional Resources