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PHY2048_11-18-09 - Chapter 15 Oscillations/18/2009...

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Chapter 15: Oscillations Lecture 33 11/18/2009
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Oscillations Goals for this Lecture: Displacement, velocity and acceleration of a simple harmonic oscillator Energy of a simple harmonic oscillator Examples of simple harmonic oscillators: spring- mass system, simple pendulum, physical pendulum, torsion pendulum Damped harmonic oscillator Forced oscillations/Resonance
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Oscillations Oscillations are a periodic, repetitive motion (of any physical variable) Examples: Mechanical oscillations : Heart beats, sound waves, earthquakes, swing set, rocking chair ... Other oscillations : Electro-magnetic, temperature stock market prices, # of students in this room, ... time Variable # student in room vs time Heart beat EKG Dow Jones 1 day 1 s 1 year
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Simple Harmonic Motion Simple Harmonic Motion (SHM) is a class of oscillations that is Periodic: repeats exactly with a period T (or a frequency f = 1/T) Described by a sinusoidal function: x(t) = x m cos( ! t + " ) time x(t) T -x m x m
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Properties of SHM Properties: Period: T [s] x(t) = x(t+T) Frequency: f [Hz] = [s -1 ] f = 1/T
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