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**Simple Harmonic Motion and Waves December 1, 2010**

PHYS16 – Lecture 33 Xkcd.com Simple Harmonic Motion and Waves December 1, 2010

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**Outline for Oscillations**

Simple Harmonic Motion Position, Velocity, Acceleration Force Energy Phase Damping Resonance Waves Mechanical waves Interference Standing waves

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**Simple Harmonic Motion – Cheat Sheet**

Position, Velocity, and Acceleration Restoring Force gives ang. freq. dependence

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**Simple Harmonic Motion: Restoring Force**

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**Example Question What is the period of a pendulum?**

Where is the restoring force the greatest? Where is tension the greatest? Restoring force – At top of swing! Tension – At bottom of swing

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**Simple Harmonic Motion: Energy**

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Energy in SHM

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Example Question A 0.5-kg mass hits a spring with a velocity of 2 m/s. The spring starts in its equilibrium position and has a spring constant of 0.5 N/m. What is the amplitude of the oscillation? A = 2 m

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**Simple Harmonic Motion: Phase**

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**Phase What happens if at t=0, x doesn’t equal 0?**

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**Simple Harmonic Motion: Damping and Resonance**

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Damping Damping – when a force (friction, air drag) causes the oscillator to lose energy A

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Resonance Resonance – when a driving force has the same frequency of oscillation as the oscillator

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Example Question 1 A mass on a spring is driven at a driving frequency (red curve) and the resulting position vs. time of the mass is given (blue curve). Which case is closest to resonance?

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Example Question 2 When would you want to have resonance or damping? When would resonance or damping be unwanted? Damping – when you don’t want oscillations: buildings, bridges Resonance – when you want to have oscillations: pushing a kid on a swing, making standing waves in cavity

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Main Points - SHM Movement is dependent upon amplitude, period and phase Restoring Force creates oscillation Energy is dependent on amplitude Damping decreases A, Resonance increases A

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Ball in a Bowl: F g F N F g F N F F Simple Harmonic Motion (SHM) Stable Equilibrium (restoring force, not constant force)

Ball in a Bowl: F g F N F g F N F F Simple Harmonic Motion (SHM) Stable Equilibrium (restoring force, not constant force)

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