29. Damped Driven Oscillators - Galileo and Einstein

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Underdamped Motion

• The point to note here is

that the damping can

cause rapid decay of the

oscillations without a

perceptible change in

the period (around

0.04% for b = 0.11, k = 4,

m = 1).

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Underdamped Motion • The point to note here is that the damping can cause rapid decay of the oscillations without a perceptible change in the period (around 0.04% for b = 0.11, k = 4, m = 1).

Underdamped Motion • Compare the curve with the equation: the successive position maxima follow an t Ae γ − exponential curve , so any maximum reached is, say, 90% of the previous maximum. • Remember the energy at maximum displacement is ½kx2 . • a − γ t ′ x = Ae cosω t

Page 1 and 2: Damped and Driven Harmonic Motion M
Page 3: Underdamped Motion • The equation
Page 7 and 8: Not So Underdamped Motion Even when
Page 9 and 10: • Doubling the damping beyond cri
Page 11 and 12: The Damped Driven Oscillator • We
Page 13: The Damped Driven Oscillator • Th

29. Damped Driven Oscillators - Galileo and Einstein

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