Torsion Pendulum<br />Tyler Cash<br />
Torsion Pendulum<br />	An object that has oscillations which are due to rotations about some axis through the object.<br />
Damped Oscillations<br />Any oscillation in which the amplitude of the oscillating quantity decreases with time. <br />
In general, torsion pendulums satisfy<br />J – Moment of Inertia<br />b – Damping Coefficient<br />c – Restoring Torque co...
Solution to the equation yields 3 cases:<br />Underdamped - many oscillations<br />Critically Damped – one oscillation<br ...
Apparatus<br />
Procedure<br />Find natural frequency (no damping) by measuring the period several times<br />Turn on damping current<br /...
Angle vs. Time Plot<br />Chi-Squared: 2.4<br />
Angle vs. Time Plot<br />Chi-Squared: 1.4<br />
Damping Constants<br />I=204 mA<br />β = .194 ± .004 radians/s<br />I = 448 mA<br />β = .581 ± .018 radians/s<br />
Critically Damped<br />Trial and error found I=1.95 A caused critical damping<br />
Damping Constant<br />Using a fixed displacement and the time for that displacement,<br />Results in<br />β =  2.51 ± .26 ...
Results<br />As the damping current increased, the damping constant increased.<br />
Forced Oscillations<br />An oscillation produced in a simple oscillator or equivalent mechanical system by an external per...
Apparatus<br />
Procedure<br />Experiment with several driving frequencies in order to find the resonance frequency of the pendulum<br />R...
Resonance frequency plot<br />Resonance Frequency approximately .54 rad/s<br />
Resonance Frequency Plot<br />Resonance Frequency approximately .52 rad/s<br />
Resonance Frequency Plot<br />Resonance Frequency approximately .51 rad/s<br />
Resonance Frequency<br />From our plots and data, we estimated the following resonance frequencies:<br />
Damping Constants<br />For driven, damped oscillators, <br />Using this formula, we calculated the damping constant.<br />
Results<br />Our results for Damping Constants are unreliable.<br />Causes?<br /><ul><li>Not enough data points near reson...
Resonance and natural frequency are so close that errors are multiplied.</li></li></ul><li>Results<br />As driving frequen...
Conclusion<br />Overall, our data accurately described the typical motion of a torsion pendulum.<br />To improve our resul...
Questions?<br />
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Torsion Pendulum

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Torsion Pendulum

  1. 1. Torsion Pendulum<br />Tyler Cash<br />
  2. 2. Torsion Pendulum<br /> An object that has oscillations which are due to rotations about some axis through the object.<br />
  3. 3. Damped Oscillations<br />Any oscillation in which the amplitude of the oscillating quantity decreases with time. <br />
  4. 4. In general, torsion pendulums satisfy<br />J – Moment of Inertia<br />b – Damping Coefficient<br />c – Restoring Torque constant<br />θ- Angle of Rotation<br />
  5. 5. Solution to the equation yields 3 cases:<br />Underdamped - many oscillations<br />Critically Damped – one oscillation<br />Overdamped – one very long oscillation<br />
  6. 6. Apparatus<br />
  7. 7. Procedure<br />Find natural frequency (no damping) by measuring the period several times<br />Turn on damping current<br />Set pendulum in motion and record angle of rotation after each oscillation<br />
  8. 8. Angle vs. Time Plot<br />Chi-Squared: 2.4<br />
  9. 9. Angle vs. Time Plot<br />Chi-Squared: 1.4<br />
  10. 10. Damping Constants<br />I=204 mA<br />β = .194 ± .004 radians/s<br />I = 448 mA<br />β = .581 ± .018 radians/s<br />
  11. 11. Critically Damped<br />Trial and error found I=1.95 A caused critical damping<br />
  12. 12. Damping Constant<br />Using a fixed displacement and the time for that displacement,<br />Results in<br />β = 2.51 ± .26 radians/s<br />
  13. 13. Results<br />As the damping current increased, the damping constant increased.<br />
  14. 14. Forced Oscillations<br />An oscillation produced in a simple oscillator or equivalent mechanical system by an external periodic driving force.<br />
  15. 15. Apparatus<br />
  16. 16. Procedure<br />Experiment with several driving frequencies in order to find the resonance frequency of the pendulum<br />Record the phase shift between the pendulum and the driving motor<br />Repeat this process over a range of damping currents<br />
  17. 17. Resonance frequency plot<br />Resonance Frequency approximately .54 rad/s<br />
  18. 18. Resonance Frequency Plot<br />Resonance Frequency approximately .52 rad/s<br />
  19. 19. Resonance Frequency Plot<br />Resonance Frequency approximately .51 rad/s<br />
  20. 20. Resonance Frequency<br />From our plots and data, we estimated the following resonance frequencies:<br />
  21. 21. Damping Constants<br />For driven, damped oscillators, <br />Using this formula, we calculated the damping constant.<br />
  22. 22. Results<br />Our results for Damping Constants are unreliable.<br />Causes?<br /><ul><li>Not enough data points near resonance
  23. 23. Resonance and natural frequency are so close that errors are multiplied.</li></li></ul><li>Results<br />As driving frequency increased, the phase shift increased.<br />At low frequencies, the phase shift was zero degrees<br />At high frequencies, the phase shift approached 180°<br />At resonance, the phase angle was 90°<br />
  24. 24. Conclusion<br />Overall, our data accurately described the typical motion of a torsion pendulum.<br />To improve our results, we suggest being more careful to take many data points around the resonance frequency.<br />
  25. 25. Questions?<br />
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