Torsion Pendulum

Physics Talk on Torsion Pendulum Experiment.
Presentation was given to Physics faculty and students

1. Torsion Pendulum Tyler Cash

2. Torsion Pendulum An object that has oscillations which are due to rotations about some axis through the object.

3. Damped Oscillations Any oscillation in which the amplitude of the oscillating quantity decreases with time.

4. In general, torsion pendulums satisfy J – Moment of Inertia b – Damping Coefficient c – Restoring Torque constant θ- Angle of Rotation

5. Solution to the equation yields 3 cases: Underdamped - many oscillations Critically Damped – one oscillation Overdamped – one very long oscillation

6. Apparatus

7. Procedure Find natural frequency (no damping) by measuring the period several times Turn on damping current Set pendulum in motion and record angle of rotation after each oscillation

8. Angle vs. Time Plot Chi-Squared: 2.4

9. Angle vs. Time Plot Chi-Squared: 1.4

10. Damping Constants I=204 mA β = .194 ± .004 radians/s I = 448 mA β = .581 ± .018 radians/s

11. Critically Damped Trial and error found I=1.95 A caused critical damping

12. Damping Constant Using a fixed displacement and the time for that displacement, Results in β = 2.51 ± .26 radians/s

13. Results Current ( mA ) Damping Constant (Radians/s) 204 .194 ± .004 448 .580 ± .018 1950 2.51 ± .26 As the damping current increased, the damping constant increased.

14. Forced Oscillations An oscillation produced in a simple oscillator or equivalent mechanical system by an external periodic driving force.

15. Apparatus

16. Procedure Experiment with several driving frequencies in order to find the resonance frequency of the pendulum Record the phase shift between the pendulum and the driving motor Repeat this process over a range of damping currents

17. Resonance frequency plot Resonance Frequency approximately .54 rad /s

18. Resonance Frequency Plot Resonance Frequency approximately .52 rad /s

19. Resonance Frequency Plot Resonance Frequency approximately .51 rad /s

20. Resonance Frequency From our plots and data, we estimated the following resonance frequencies: Damping Current ( mA ) Resonance Frequencies .54 ± .09 396 .52 ± .02 800 .51 ± .03

21. Damping Constants For driven, damped oscillators, Using this formula, we calculated the damping constant.

22. Results Resonance Frequency ( rad /s) Damping Constant ( rad /s) .54 ± .09 .594 ± .435 .52 ± .02 .202 ± .780 .51 ± .03 .143 ± .830 Our results for Damping Constants are unreliable. Causes? Not enough data points near resonance Resonance and natural frequency are so close that errors are multiplied.

23. Results As driving frequency increased, the phase shift increased. At low frequencies, the phase shift was zero degrees At high frequencies, the phase shift approached 180° At resonance, the phase angle was 90°

24. Conclusion Overall, our data accurately described the typical motion of a torsion pendulum. To improve our results, we suggest being more careful to take many data points around the resonance frequency.

25. Questions?