Teachspin - Torsional Oscillator: The Instrument

Torsional Oscillator

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Simple Harmonic Oscillation Made Visible, Tangible, Accessible, Measurable

The Aluminum Rotor is clamped at the midpoint of the wire and other parts are attached to it.
The Copper Disc both contributes to the moment of inertia and interacts with the magnetic brakes.
A scale on the edge of the copper disc allows visual measurement of angular deflection in radians
Moveable magnetic brakes on either side provide variable eddy-current magnetic damping
Helmholtz coils interact with a dipole mounted on the rotor both to provide magnetic torques and to measure velocity.
Circuit Boards mounted beneath the system provide the non-contact capacitive angular-position transducer

Motivated by the central role that the Simple Harmonic Motion plays in physics, and in physics education, TeachSpin has developed an apparatus that makes visible, tangible, accessible and MEASURABLE all the features important to the physics of Simple Harmonic Motion. Our new Torsion Oscillator was designed, from the ground up, to be a premier teaching tool for the physics of the Simple Harmonic Oscillator at every level.

An overview of the apparatus:

We've chosen to exploit simple harmonic motion in angle.
The aluminum 'rotor' structure is attached at the midpoint of a taut steel wire.
A copper disc, centered on the wire, is mounted on the rotor.
Torsional elasticity of the wire provides the 'spring constant' of the SHO.
Rotational inertia of the rotor and copper disc provide the 'mass' of the SHO.
Both the spring constant and the "mass" can be changed by the user.
- Four wires of different diameters, and thus different torsional constants, are included. This allows the "spring constant" to be varied over an order of magnitude.
- Extra weights, machined to produce easily calculated rotational inertia increments, are included.
Moveable magnets mounted on the wooden frame interact with the copper disc to create variable eddy-current damping.
Helmholtz coils are attached to the cabinet so that their axis passes both through the steel wire and through the center of a magnetic dipole system mounted on the rotor.
Pulleys (not shown) mount to the outside of the cabinet at the level of the copper disc.
Pulleys, strings, masses, and hangers are provided for static torque calibration.

Close-Up View of Active Apparatus

Distinctive features of the Rotor System:

A non-contact capacitive angular-position transducer provides real-time analog angular-position information about the system to an accuracy of better than 1.0%.
The rotor is equipped with a 'radian protractor', allowing student calibration of the angular position sensor.
A real-time emf proportional to the instantaneous angular velocity of the rotor is developed by the motion of the dipole on the rotor relative to the fixed set of coils.
The magnet-in-coil system can be separately calibrated for sensitivity to angular velocity, and for torque per unit drive current. (In the process, students can verify the reciprocity theorem relating these two constants. They can even learn one method for the first-principles measurement of a magnetic moment.)

These features allow students to have direct access to the instantaneous 'position' and 'velocity' outputs of the system. They can view in real time (on an oscilloscope in the XY-display mode, or on a computer) the state of the oscillator in the 'phase plane'

Because we picked a mechanical system that involves no frictional or sliding contact with the rotor, our SHO corresponds to a high-Q oscillator. (In the absence of deliberate damping, our Torsional Oscillator displays a Q of over 100.)

Three independent damping systems:
Students can investigate the various transient or driven responses of the oscillator to each of the three available damping systems.

Eddy-current magnetic-damping 'brakes' provide a damping force that's linear in velocity. This damping is adjustable in magnitude, from negligible to beyond-critical damping;
Damping by sliding friction yields a damping force that's independent of the velocity's magnitude;
Paddles-on-arms can be easily attached allowing investigation of fluid damping by air which gives a damping force approximately quadratic in velocity.

Close-Up View of Electronics Panel

Helmholtz Coil/Dipole Modes of operation set from electronics box:

Toggle set to Velocity Readout gives angular velocity.
Toggle set to Coil Drive allows external drive by arbitrary analog electrical waveforms.