Torsion Pendulum
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Torsion Pendulum

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Physics Talk on Torsion Pendulum Experiment.

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

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Torsion Pendulum Torsion Pendulum Presentation Transcript

  • Torsion Pendulum
    Tyler Cash
  • Torsion Pendulum
    An object that has oscillations which are due to rotations about some axis through the object.
  • Damped Oscillations
    Any oscillation in which the amplitude of the oscillating quantity decreases with time.
  • In general, torsion pendulums satisfy
    J – Moment of Inertia
    b – Damping Coefficient
    c – Restoring Torque constant
    θ- Angle of Rotation
  • Solution to the equation yields 3 cases:
    Underdamped - many oscillations
    Critically Damped – one oscillation
    Overdamped – one very long oscillation
  • Apparatus
  • 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
  • Angle vs. Time Plot
    Chi-Squared: 2.4
  • Angle vs. Time Plot
    Chi-Squared: 1.4
  • Damping Constants
    I=204 mA
    β = .194 ± .004 radians/s
    I = 448 mA
    β = .581 ± .018 radians/s
  • Critically Damped
    Trial and error found I=1.95 A caused critical damping
  • Damping Constant
    Using a fixed displacement and the time for that displacement,
    Results in
    β = 2.51 ± .26 radians/s
  • Results
    As the damping current increased, the damping constant increased.
  • Forced Oscillations
    An oscillation produced in a simple oscillator or equivalent mechanical system by an external periodic driving force.
  • Apparatus
  • 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
  • Resonance frequency plot
    Resonance Frequency approximately .54 rad/s
  • Resonance Frequency Plot
    Resonance Frequency approximately .52 rad/s
  • Resonance Frequency Plot
    Resonance Frequency approximately .51 rad/s
  • Resonance Frequency
    From our plots and data, we estimated the following resonance frequencies:
  • Damping Constants
    For driven, damped oscillators,
    Using this formula, we calculated the damping constant.
  • Results
    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.
  • 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°
  • 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.
  • Questions?