lecture36[1]

# lecture36[1] - Damped Oscillations and Resonance Serway...

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1 Physics 1D03 Damped Oscillations and Resonance Serway 15.6, 15.7 • Damped Harmonic Oscillation • Forced Oscillations • Resonance Practice: Chapter 15, problems 37, 41 Physics 1D03 x t x t SHM: x(t) = A cos ω t Motion continues indefinitely. Only conservative forces act, so the mechanical energy is constant. Damped oscillator: dissipative forces (friction, air resistance, etc. ) remove energy from the oscillator, and the amplitude decreases with time.

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2 Physics 1D03 ) cos( ) ( ) ( 2 0 φ ω + = - t e A t x t m b Weak damping: Damped Oscillator: Drag force f = - b v x t Amplitude decreases exponentially with time Physics 1D03 Without damping: the angular frequency is 2 2 0 2 2 2 - = - = m b m b m k The frequency is slightly lower with damping. m k = 0 With damping:
3 Physics 1D03 Example : A mass on a spring oscillates with initial amplitude 20 cm. After 10 seconds, the amplitude is 10 cm. Question:

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## This note was uploaded on 12/14/2010 for the course ENGINEERIN 1D03 taught by Professor N.l.mckay during the Spring '10 term at McMaster University.

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lecture36[1] - Damped Oscillations and Resonance Serway...

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