5.3.3 Damping

An oscillation is amped when an external force that acts on the oscillator has the effect of reducing the amplitude of its oscillations. E.g a pendulum moving through air experiences air resistance which damps the oscillations until the pendulum comes to rest.

When amping forces are small the amplitude of the oscillator gradually decreases with time but the period (T) is almost unchanged. This is light damping.

For larger damping forces the amplitude decreases significantly and the period also increases slightly. This is heavy damping (e.g is a pendulum was stopped with water). 

Very heavy damping occurs if we were to damp the pendulum with for example treacle/oil. Eventually there would be no oscillatory motion. Instead the oscillator would slowly move towards its equilibrium position.

The x-t graph is as follows:

When a system is displaced and allowed to oscillate without any external forces its motion is referred to as free oscillation. The frequency of the free oscillation is known as the natural frequency of the oscillator. A forced oscillation is one in which a periodic driver force is applied to an oscillator. The object will vibrate at the frequency of the driving force (the driving frequency).

If the driving frequency is equal to the natural frequency of an oscillating object resonance will occur. This causes the amplitude of the oscillations to increase dramatically and, if not damped, the system may break. The greatest possible transfer of energy from the driver to the forced oscillator occurs at the resonant frequency. This is why the amplitude of the forced oscillator is maximum. Resonance examples include:

• Tacoma Narrows Bridge
• Types of tuning circuits (e.g in car radios to select the correct frequency radio wave signal)
• Many clocks keep time using the resonance of a pendulum
• Musical instruments have bodies that resonate to produce louder notes
• MRI enables diagnostic scans of inside our bodies without surgery/the use of harmful X-rays (MRI stands for magnetic resonance imaging)

NOTE: damping a forced oscillation has the effect of reducing the maximum amplitude at resonance. The degree of damping also has an effect on the frequency of the driver when maximum amplitude occurs.

Amplitude-driving frequency graphs:

• Light damping: the maximum amplitude occurs at the natural frequency (fo) of the forced oscillator.
• As the amount of damping increases:
• the amplitude of vibration at any frequency decreases
• the maximum amplitude occurs at a lower frequency that fo
• the peak on the graph becomes flatter and broader

Image sources: Kerboodle OCR A Physics textbook