Driven Damped Oscillator

Single air track glider, with and without variable frequency driver, variable damping, and oscilloscope position vs. time display.

What It Shows

With one end of the car attached via a spring to the end of the track and the other end of the car coupled (via a similar spring) to a driving motor, we can see how the car behaves when it is driven below, at, and above the resonance frequency. Markings on the motor help to show the phase relationships between the driver and car at different frequencies. A storage scope tracks the motion of the car (see Setting It Up section for how this is done). The car has a fin that can be partially immersed in a trough filled with glycerol to add damping.

With both ends of the car attached to the track, the effects of various amounts of damping on the car's motion can be observed. When the motion is underdamped, the amplitude of the car's oscillation decreases exponentially over several cycles; when the motion is overdamped, the car reaches its equilibrium position without any oscillation; in the critically damped case, the car settles down to its final equlibrium position in the least amount of time. The storage scope can illustrate these three regimes by drawing position vs time graphs.

Setting it up

The air track, driving motor1, and motor speed control2 are all permanently mounted as a single unit. A bare copper wire, about 4 inches in length, protrudes downward from the side of the car, allowing for the car to be electrically connected to a trough of water that sits alongside the track. When a constant voltage is applied across the water via a 12V battery, the oscilloscope probe can be electrically connected to the car to give a voltage reading. The schematic below illustrates the important details of how this is achieved.


Note that a 6V battery must be connected in series to the scope probe so that the probe reads 0V when the car is in the equilibrium position. Tap water provides adequate conductivity. The electrical connection to the car is made by attaching an alligator clip to one of the springs. A low-pass filter is attached to the probe to reduce noise from the driving motor.

1 Leeson Permanent Magnet D.C. Gearmotor Model CM24D25NZ3C
2 Leeson Speedmaster