PHY2048_11-20-09 - Chapter 15 Oscillations/20/2009...

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Chapter 15: Oscillations Lecture 34 11/20/2009
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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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Energy in SHM What is the energy contained in a simple harmonic oscillator? Potential energy: U spring = 1/2kx 2 U(t) = 1/2kx m 2 cos 2 ( ! t+ " ) Kinetic Energy: K mass = 1/2 mv 2 K(t) = 1/2 m ! 2 x m 2 sin 2 ( ! t + " ) = 1/2 k x m 2 sin 2 ( ! t + " ) Total Mechanical Energy: E tot (t) = U(t) + K(t) = 1/2 k x m 2 [cos 2 ( ! t + " ) + sin 2 ( ! t + " )] E tot (t) = 1/2 k x m 2 = 1/2 m ! 2 x m 2 = constant
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Angular SHM A torsion pendulum is an oscillating system similar to a spring, except that an object of rotational inertia I rotates/twists around a wire which exerts a restoring torque: # = - $% ( $ is the torsion constant)
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This note was uploaded on 02/12/2010 for the course PHY PHY taught by Professor Mueller during the Fall '09 term at University of Florida.

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PHY2048_11-20-09 - Chapter 15 Oscillations/20/2009...

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