9702 · 17.3
Damped and forced oscillations, resonance — FAQ
Frequently asked questions for 9702 Damped and forced oscillations, resonance. Direct answers first, then deeper explanation — then practise with marking.
Why is damping crucial in real-world oscillating systems?
Damping is crucial because it controls and limits the amplitude of oscillations, preventing them from growing indefinitely, especially at resonance. This helps prevent structural failure in bridges, reduces unwanted vibrations in machinery, and allows systems to return to equilibrium predictably.
What's the main difference between natural frequency and driving frequency?
The natural frequency is an intrinsic property of a system, the frequency at which it oscillates freely without external influence. The driving frequency is the frequency of an external periodic force applied to the system, forcing it to oscillate. Resonance occurs when these two frequencies match.
How can engineers prevent destructive resonance in structures?
Engineers prevent destructive resonance by designing structures with natural frequencies far away from any expected driving frequencies (e.g., wind, seismic activity). They also incorporate damping mechanisms, such as shock absorbers or tuned mass dampers, to reduce amplitude peaks if resonance is unavoidable.
What is the formula for power dissipated by damping in SHM?
The average power dissipated by a damping force F = -bv (where b is the damping coefficient and v is velocity) in simple harmonic motion is given by <P> = ½ * b * (Aω)², where A is the amplitude and ω is the angular frequency.