If an oscillator is displaced and then released it will begin to vibrate. If no more external forces are applied to the system it is a free oscillator. If a force is continually or repeatedly applied to keep the oscillation going, it is a forced oscillator.

Let’s use the example of a wine glass. If you flick the glass and let it ring, the glass acts as a free oscillator. If you wet your finger and run it around the glass rim, your finger will force continuous vibration by repeatedly slipping and sticking (very fast). This slip-stick excitation is the same as takes place when violin players use a violin bow to drive their strings.

In this extract from a slow motion video, a glass is driven into forced oscillation. Water was poured into the glass, as it vibrates very visibly and makes the motion of the walls of the glass very clear.

Going back to our example of a playground swing: if the swing is pushed just once it acts as a free oscillator, but the damping provided by air resistance and losses at the pivots, mean it will eventually stop swinging. If the swing is pushed each time it reaches a certain point it behaves as a forced oscillator and will continue to swing for as long as energy is supplied. This is shown below:

The pusher normally pushes the swing every time it reaches its maximum negative displacement. What would happen if he pushed the swing more often, or less often?

If the swing is simply lifted and let go it will swing with a natural frequency. This frequency is determined by a number of factors, of which the most important is the length of the swing from pivot to seat. How does this natural frequency determine when the pusher should push?

If the swing is pushed with a long interval between pushes, the swing will not receive enough energy to replace that lost by damping. Also, the pushes may be out of synch with the swing’s natural period of oscillation. This might mean that sometimes the pusher would be pushing when the swing is in the wrong location.

If the person pushes with a shorter interval between pushes, he may again be out of synch with the natural frequency of the swing.

The natural frequency that the swing wants to oscillate at is called its resonant frequency. If the pusher pushes at the swing’s resonant frequency, the amplitude of oscillation will build up. With each period, the pusher will add more energy to the system. Eventually, what usually happens is that energy supply equals energy loss (to damping), and the amplitude stabilises at some large value. If there is insufficient damping in the system the oscillation amplitude can get very large and something dramatic may happen

Understanding free and forced vibrations is vital to much work in acoustical engineering, whether you’re working for a car manufacturer trying to get rid of an annoying rattling sound or as Tom describes below, trying to stop the rumble of train vibrations getting into a building.

When we’re trying to prevent ground vibrations from underground trains getting into a building, we’re looking at forced oscillation. One way of preventing these vibrations entering a building is to build it on springs. The frequency of vibration comes from the train. The most tricky situation is when a forcing frequency match a natural resonance frequency in the building, because that will amplify the vibration rather than reduce it.

Tomasz Galikowski

Career case study: read about Tom’s job dealing with noise and vibration in the built environment

Here’s a slow-motion video of a wine glass driven into forced oscillation at its resonant frequency. This time it’s forced by a high-power loudspeaker driven by a sine-wave generator. To vibrate, the glass walls must bend, and glass won’t bend too far before it breaks. If you want to know how to break a glass with sound, here are our instructions for this classic resonance demo.

A little more damping (e.g. a rubber band around the glass) could stop this happening by reducing the resonant vibration amplitude. If the oscillating system was the wing attached to the jet plane taking you on holiday, you would be hoping that the designer had incorporated sufficient damping into the structure!