# Physics Today

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Introducing...

TeachSpin's Torsional Oscillator is a first-class way to teach and learn about simple harmonic motion, and by itself, it permits dozens of experimental investigations.  But from the beginning, we've realized that the addition of some rather simple external electronics allows the Torsional Oscillator to become part of an electro-mechanical system which is ideal for teaching physics students about the concept, and the uses, of feedback.  So we have introduced the TO's Auxiliary Electronics, a simple package which extends the capabilities of the TO into new domains, and makes new kinds of teaching and learning possible.

What's special about the TO itself is that it produces a real-time analog output voltage proportional to the (angular) coordinate of a system undergoing simple harmonic motion, and that it accepts a real-time analog input current which creates a proportional torque on that system.  So the Auxiliary Electronics permits students to take that TO output, to modify it electronically in the AE, and to feed it back into the TO as a drive.  Better still, they can understand just how the feedback ought to affect the properties of the TO.  Result:  TO+AE combination can display behavior that's not available in the TO itself.

One of the most glamorous outcomes made possible by the TO+AE combination is the abolition of damping, so that the TO's oscillations are no longer damped sinusoids, but instead turn into undampled continuing oscillations of the TO, at its own natural frequency.  The result is a 'torsional clock', operating as an electro-mechanical oscillator, in which the TO provides the timing, while the AE provides the energy needed to keep the oscillations from decaying due to residual damping.  Such a clock is capable of remarkable timing performance, and is also an illustration of the general technique of applying feedback to a lightly damped system to turn the comination into an oscillator.

# The Relaxation Times

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# TORSIONAL OSCILLATOR AUXILIARY ELECTRONICS

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