Principle

If an oscillating system is allowed to swing freely it is
observed that the decrease of successive maximum amplitudes is
highly dependent on the damping. If the oscillating system is
stimulated to swing by an external periodic torque, we observe that
in the steady state the amplitude is a function of the frequency
and the amplitude of the external periodic torque and of the
damping. The characteristic frequencies of the free oscillation as
well as the resonance curves of the forced oscillation for
different damping values are to be determined

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

Designed for large and clear shadow projection while experimenting



Tasks


A. Free
oscillation



To determine the oscillating period and the characteristic
frequency of the undamped case.

To determine the oscillating periods and the corresponding
characteristic frequencies for different damping values.
Successive, unidirectional maximum amplitudes are to be plotted as
a function of time. The corresponding ratios of attenuation, the
damping constants and the logarithmic decrements are to be
calculated.

To realise the aperiodic case and the creeping.



B. Forced
oscillation



The resonance curves are to be determined and to be represented
graphically using the damping values of A.

The resonance frequencies are to be determined and are to be
compared with the resonance frequency values found before
hand.

The phase shifting between the torsion pendulum and the
stimulating external torque is to be observed for a small damping
value assuming that in one case the stimulating frequency is far
below the resonance frequency and in the other case it is far above
it.


What you can learn about


Angular frequency

Characteristic frequency

Resonance frequency

Torsion pendulum

Torsional vibration

Torque and restoring torque

Damped/ undamped free oscillation

Forced oscillation

Ratio of attenuation/ decrement

Damping constant

Logarithmic decrement

Aperiodic case

Creeping