PURPOSE: To demonstrate amplitude "jumps" and resonance hysteresis in Duffing's equation.

DESCRIPTION: The clamped hacksaw blade with a magnet and mirror attached to its free end is a non-linear oscillator. A laser reflected off the mirror is used as an indicator of the motion. Driving the oscillator with a Wavetek sine generator using a small coil one can observe: (1) sudden changes in amplitude as the frequency is very slowly changed, and (2) hysteresis in the oscillation amplitude at a given frequency, which depends on whether the frequency is being increased or decreased. The frequency can be most readily measured with a digital meter measuring the period of the driving sine wave.

SUGGESTIONS: Vary the frequency SLOWLY. This is an extremely sensitive effect.

REFERENCES: (PIRA 3A95.45) See Demonstration Reference File for a plethora of articles covering the topics of non-linear oscillators and amplitude jumps.

EQUIPMENT: Hack saw blade oscillator assembly, laser, Wavetek and digital meter, as photographed.

SETUP TIME: 10 min.

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