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Push a child on a swing at just the right rate and the swing goes higher and higher with barely any effort; push at the wrong rate and nothing much happens at all. That sensitivity to timing is resonance, and engineers spend enormous effort making sure it never happens by accident in bridges or buildings.
What you'll be able to do
A occurs at a system’s own natural frequency with no continuing external force. A is driven at a chosen frequency, which may differ from the natural frequency.
removes energy from an oscillating system. lets amplitude decay gradually over many cycles; returns the system to equilibrium in the shortest time without oscillating; returns to equilibrium without oscillating, but more slowly than critical.
Tip — Critical damping is the fastest non-oscillating return to equilibrium — heavier damping than critical actually takes LONGER, not shorter.
When driving frequency approaches a system’s natural frequency, the amplitude of the forced oscillation grows dramatically — . More damping lowers the peak amplitude, broadens the resonance curve, and shifts the peak to a slightly lower frequency.
Tip — Three effects of more damping on resonance: lower peak, broader peak, peak shifts slightly lower — remember all three together.
Resonance is used deliberately in musical instruments and microwave ovens, but can be destructive: London’s Millennium Bridge had to close shortly after opening when pedestrians’ footsteps synchronised with, and amplified, its natural sideways sway. Engineers combat unwanted resonance by keeping a structure’s natural frequency well away from any likely driving frequency, or by adding damping.
Common mistakes to avoid
Key takeaways
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