Concepts

Driven harmonic oscillators, normal modes

Overview

A variable-speed motor drives a set of identical oscillators coupled by identical springs. The masses rest on an air track for low-friction movement. Several normal modes of this 1D lattice can be observed by changing the motor speed. Masses can be clamped to the oscillators to simulate a lattice with unequal-mass particles.

Details

Equipment

• [1] Air track
• [2] Cart
• [6] Oscillator
• [6] Spring
• [1] Spring with a string
• [3] Mass
• [1] Motor
• [1] Variac
• [1] Reversed vacuum
• [2] Hose
• [1] Hose coupler
• [1] Hose clamp
• [1] Slot-head screwdriver
• Power bar
• Extension cord
  

Classroom Assembly

1. Place the air track in position on the carts.
2. Join the vacuum to the track using the hoses and hose coupler.
3. Plug the vacuum into the power bar using the extension cord and secure the power bar to one of the carts. The power bar will act as a convenient power switch for the vacuum.
4. Plug the power bar into a wall outlet.
5. Place the variac and motor on the same cart as the power bar.
6. Plug the motor into the variac and the variac into the power bar.
7. Turn on the vacuum.
8. Place the oscillators onto the air track. Add springs to join them together and join one end to the air track.
9. Use the spring with a string to join an oscillator to the motor.
10. Turn off the vacuum.
    

Script

1. Turn on the vacuum.
2. Turn on the variac and dial it to the first mode you want to observe. The modes are approximately at 16 V, 30 V, 60 V, 87 V, 100 V, and 112 V.
   
3. Repeat for the other modes you want to see. You may need to stop the oscillators with your hands or by turning off the variac and vacuum so that you don't get previous modes around as transients.
   
4. Dial the variac to a point between two modes to observe a superposition of the two modes.
5. Turn off the variac.
6. Turn off the vacuum.
   

Additional Resources