Simple Harmonic Motion and Waves December 1, 2010

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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

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

Simple Harmonic Motion – Cheat Sheet Position, Velocity, and Acceleration Restoring Force gives ang. freq. dependence

Simple Harmonic Motion: Restoring Force

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 http://upload.wikimedia.org/wikipedia/en/thumb/a/a8/Pendulum.png/300px-Pendulum.png

Simple Harmonic Motion: Energy

Energy in SHM http://www.farraguttn.com/science/milligan/APPhys/SHMOver_files/image022.jpg

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

Simple Harmonic Motion: Phase

Phase What happens if at t=0, x doesn’t equal 0? http://www.learner.org/courses/mathilluminated/images/units/10/1858.png

Simple Harmonic Motion: Damping and Resonance

Damping Damping – when a force (friction, air drag) causes the oscillator to lose energy A http://beltoforion.de/pendulum_revisited/Damped_oscillation_graph2.png

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

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?

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

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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