Principle

If an oscillating system is allowed to oscillate freely, we can observe that the decrement of successive maximum amplitudes strongly depends on the damping value. If the oscillating system is caused to oscillate by an external torsional oscillation, we can observe that the amplitude in a stationary state is a function of the frequency and amplitude of the external periodic torsional oscillation and of the damping value. The aim of this experiment is to determine the characteristic frequency of the free oscillation as well as the resonance curve of a forced oscillation.

Benefits

• Long-lasting oscillation due to ball bearings
• Damping via abrasion-resistant eddy current brake
• Simple illustration of the elementary principle of forced oscillations
• Suitable for demonstration and student experiments as well
• Easy measurement and evaluation via movement tracking software

Tasks

A. Free oscillation

1. Determination of the period of oscillation and characteristic frequency for the undamped case.
2. Determination of the period of oscillation and corresponding characteristic frequencies for various damping values. Calculation of the corresponding ratios of damping, damping constant, and logarithmic decrement.
3. Realisation of the aperiodic case and creeping case.

B. Forced oscillation

1. Determination of the resonance curve and graphical representation of the resonance curve by way of the damping values of A.
2. Observation of the phase difference between the torsional pendulum and the exciting, external rotation for a small damping value with different excitation frequencies.

Learning objectives

• Angular velocity
• characteristic frequency
• resonance frequency
• torsional pendulum
• torsional oscillation
• restoring torque
• damped/undamped free oscillation
• forced oscillation
• ratio of damping/decrement
• constant damping
• logarithmic decrement
• aperiodic case
• creeping