PHY2048_11-23-09 - Chapter 15: Oscillations Lecture 35...

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Chapter 15: Oscillations Lecture 35 11/23/2009
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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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Consider an object undergoing uniform circular motion: Uniform angular velocity ! the angle " increases linearly with time: " = ! t + # The x/y positions of the object is: x = R cos " , y = R sin " . Then x(t) = R cos " = R cos( ! t + # ) y(t) = Rsin " = Rsin( ! t+ # ) = Rcos( ! t+ # - ! /2) The velocity along the x/y-axis: v x = - ! R sin( ! t + # ), v y = - ! R sin( ! t+ # - ! /2) The acceleration along the x/y-axis: a x = - ! 2 R cos( ! t+ # ), a y = - ! 2 Rcos( ! t+ # - ! /2)
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Damped Simple Harmonic Motion So far we have considered oscillation without friction. If drag or friction act on the
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PHY2048_11-23-09 - Chapter 15: Oscillations Lecture 35...

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