A) In steady state, does a damped, driven oscillator oscillate at the frequency

Question

A) In steady state, does a damped, driven oscillator oscillate at the frequency of the driving force, the natural frequency of the oscillator or neither of these frequencies? B) Ella Fitzgerald could break a wine glass with her voice but Louis Armstrong could not. Is this likely because Ella could sing louder than Louis? Justify your answer. C) What happens to the width of the average-power-delivered vs driving frequency curve if the damping is increased? D) What happens to the height of the average-power-delivered vs driving frequency curve if the damping is increased? E) Describe the resonance effect using one sentence. Consider a damped driven oscillator with a quality factor of 20. Find the ratio of the average power delivered to the oscillator at a given driving frequency ohm to that delivered on resonance for the cases indicated below. That is, find (P_del (ohm))/P_del (ohm = omega)) for the following cases. A) ohm = omega - gamma/2 B) ohm = omega + gamma/2 D) ohm = omega + 2 gamma E) ohm = omega + 5 gamma

Explanation / Answer

A) Since the oscillator is in steady state or in eqilibrium, it will neither loose energy not gain energy. That means, it will remains at the point with minimum energy and thus, the oscillator will oscillate at the natural frequency of the oscillator.

B) The reason why Ella could break the glass while Louis couldn't is that the Ella's voice is producing the same frequency at which the molecules of glass vibrates. So, the displacement in air particles around the glass causes a wave which breaks the glass.

C) Since damping is increased, that means that the energy of the system is decresaing, and hence more power is needed to make the system return bacck to the steady state and hence the width of the average power delievered will increase.

D) Because energy of the system is decreasing, the maximum power a system can have in staedy state will decrease too. This means that the height of the average power delivered versus frequency will decrease as the damping increases.

E) Resonance effect refers to the matching of the natural frequency of two different sources at their steady state.

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