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Harmonic Motion

Harmonic Motion. Describe the motion of a rider on a ferris wheel relative to the ground. Describe the motion of a buoy in an ocean relative to the ocean floor:. Describe the motion of a vibrating horizontal guitar string. Describe the motion of a piston in a cylinder.

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Harmonic Motion

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  1. Harmonic Motion

  2. Describe the motion of a rider on a ferris wheel relative to the ground.

  3. Describe the motion of a buoy in an ocean relative to the ocean floor:

  4. Describe the motion of a vibrating horizontal guitar string.

  5. Describe the motion of a piston in a cylinder.

  6. Describe the motion of the mass in a mass-spring system:

  7. Harmonic Motion • simple harmonic motion – repetitious motion that would continue without stopping if there were no outside forces on the object

  8. Harmonic Motion • “if there were no outside forces on the object”

  9. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum

  10. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity

  11. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system

  12. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system – gravity, friction

  13. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system – gravity, friction • vibrating guitar string

  14. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system – gravity, friction • vibrating guitar string - tension

  15. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system – gravity, friction • vibrating guitar string - tension • floating buoy

  16. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system – gravity, friction • vibrating guitar string - tension • floating buoy • ferris wheel

  17. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system – gravity, friction • vibrating guitar string - tension • floating buoy • ferris wheel – mechanical/human

  18. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system – gravity, friction • vibrating guitar string - tension • floating buoy • ferris wheel – mechanical/human • piston in a cylinder

  19. Harmonic Motion • “if there were no outside forces on the object” • swinging pendulum - gravity • mass in a spring-mass system – gravity, friction • vibrating guitar string - tension • floating buoy • ferris wheel – mechanical/human • piston in a cylinder – friction/ human

  20. Harmonic Motion • We know that the motion of objects with simple harmonic motion can be represented by a sine or cosine function. • Here’s why: If you were to trace out the object’s motion over time (or some other x-coordinate quantity), the result would be a sine or cosine function.

  21. Harmonic Motion • Imagine attaching a pencil to a guitar string, setting the string into vibration while sliding a sheet of paper to the right underneath the string and pencil. • Or imagine attaching a pencil to the outside edge of a circular object and sliding a sheet of paper to the right while the circle was turning counterclockwise.

  22. Harmonic Motion • If we know some information about the object’s motion, typically the position at some time and its frequency, then we can write an equation that will model its motion.

  23. Harmonic Motion • Problem - solving strategy: • make and label a diagram • make and label a sine or cosine function graph • write an equation to represent the graph • answer the question

  24. Harmonic Motion A buoy floats in a harbor at a location where the water depth is 26 ft. As waves pass the buoy it rises and falls. The buoy moves a total of 8 ft from its lowest to its highest point every 12 seconds. Assume the buoy is at its low point at t = 0. Find the height of the buoy after 15 seconds.

  25. Harmonic Motion Sketch a diagram:

  26. Harmonic Motion Sketch a graph to represent the motion:

  27. Harmonic Motion Write a sine or cosine equation: Answer the question:

  28. Harmonic Motion A mass in a spring-mass system is at rest 5 ft from a 10 ft ceiling. The mass is given a push up at time, t = 0. The mass is 2 ft from the ceiling at its highest point and it takes 4 seconds to complete a cycle and return to its starting position. What is the mass’ height 10 seconds after being set into motion?

  29. Harmonic Motion Sketch a diagram:

  30. Harmonic Motion Sketch a graph to represent the motion:

  31. Harmonic Motion Write a sine or cosine equation: Answer the question:

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