B.4 - Forced vibrations and resonance
Essential idea: In the real world, damping occurs in oscillators and has implications that need to be considered.

Resonance: A Perfect Experiment from youtube.com by perihelion.gr Published on 10 Nov 2012

Nature of science:
Risk assessment: The ideas of resonance and forced oscillation have application in many areas of engineering ranging from electrical oscillation to the safe design of civil structures. In large-scale civil structures, modelling all possible effects is essential before construction. (4.8)

• Natural frequency of vibration
• Q factor and damping
• Periodic stimulus and the driving frequency
• Resonance

Applications and skills:
• Qualitatively and quantitatively describing examples of under-, over- and criticallydamped oscillations

• Communication through radio and television signals is based on resonance of the broadcast signals

• Science and technology meet head-on when the real behaviour of damped oscillating systems is modelled
Graphically describing the variation of the amplitude of vibration with driving frequency of an object close to its natural frequency of vibration
• Describing the phase relationship between driving frequency and forced oscillations
• Solving problems involving Q factor
• Describing the useful and destructive effects of resonance

• Only amplitude resonance is required

Data booklet reference:
• Q = 2 π (energy stored / energy dissipated per cycle)
• Q = 2π × resonant frequency × (energy stored / power loss)

• Aim 6: experiments could include (but are not limited to): observation of sand on a vibrating surface of varying frequencies; investigation of the effect of increasing damping on an oscillating system, such as a tuning fork; observing the use of a driving frequency on forced oscillations
• Aim 7: to investigate the use of resonance in electrical circuits, atoms/molecules, or with radio/television communications is best achieved through software modelling examples