Driven Power Consider a damped oscillator, with natural frequency wo and 6. damping constant B both fixed, that is driven by a force F(t) = Fo Cos(wt). (a) Find the rate P(t) at which F(t) does work and show that the average rate (P) over any number of complete cycles is mBw2 A2. (b) Verify that this is the same as the average rate at which energy is lost to the resistive force. (c) Show that as w is varied (P) is maximum when w = wo; that is, the resonance of the power occurs at w = wo (exactly).
Driven Power Consider a damped oscillator, with natural frequency wo and 6. damping constant B both fixed, that is driven by a force F(t) = Fo Cos(wt). (a) Find the rate P(t) at which F(t) does work and show that the average rate (P) over any number of complete cycles is mBw2 A2. (b) Verify that this is the same as the average rate at which energy is lost to the resistive force. (c) Show that as w is varied (P) is maximum when w = wo; that is, the resonance of the power occurs at w = wo (exactly).
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Transcribed Image Text:Driven Power Consider a damped oscillator, with natural frequency wo and
6.
damping constant B both fixed, that is driven by a force F(t) = Fo Cos(wt).
(a) Find the rate P(t) at which F(t) does work and show that the average rate (P) over
any number of complete cycles is mBw2 A2.
(b) Verify that this is the same as the average rate at which energy is lost to the resistive
force.
(c) Show that as w is varied (P) is maximum when w = wo; that is, the resonance of the
power occurs at w = wo (exactly).
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