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Understanding Simple Harmonic Motion and Waves: Key Concepts and Applications

This comprehensive lecture covers the fundamentals of Simple Harmonic Motion (SHM) and waves, highlighting essential concepts like position, velocity, acceleration, force, energy, phase, damping, and resonance. It explains the restoring force in SHM using examples such as pendulums and oscillating masses on springs. Damping effects and resonance conditions are also discussed, along with various real-world applications. The lecture emphasizes the importance of amplitude, period, phase, and energy in oscillatory motion, offering insights into when to utilize or mitigate these phenomena.

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Understanding Simple Harmonic Motion and Waves: Key Concepts and Applications

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Presentation Transcript

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

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

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

  4. Simple Harmonic Motion:Restoring Force

  5. 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

  6. Simple Harmonic Motion:Energy

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

  8. 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

  9. Simple Harmonic Motion:Phase

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

  11. Simple Harmonic Motion:Damping and Resonance

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

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

  14. 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?

  15. 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

  16. 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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