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Simple Harmonic Motion: Understanding Periodic Motion in Physics

Learn about the concept of simple harmonic motion, its characteristic quantities, and how to calculate the period of a mass on a spring or a pendulum. Discover the relationship between displacement, amplitude, frequency, velocity, and acceleration in this fascinating physics phenomenon.

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Simple Harmonic Motion: Understanding Periodic Motion in Physics

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  1. Simple Harmonic Motion Physics Mrs. Coyle

  2. Periodic Motion

  3. Periodic Motion http://www.cleonis.nl/physics/inertosc_img/harmonic_oscillation.gif

  4. SimpleHarmonicMotion: • Is aperiodic motion that repeats at constant frequency. • Has a restoringforce thatacts to restore the oscillator to equilibrium. F=-kx Hooke’s Law x: displacement from equilibrium

  5. Characteristic Quantities of Simple Harmonic Motion • Displacement: distance from equilibrium. • Amplitude: maximum displacement

  6. Characteristic Quantities of Simple Harmonic Motion • Frequency: oscillations per unit time • Unit: 1/sec =Hertz • Period: time to complete one oscillation • Unit: sec f=1/T T=1/f

  7. SimpleHarmonicMotion • Velocity: • maximum as it passes through equilibrium • zero as it passes through the extreme positions in its oscillation. • Acceleration: a=F/m = -kx/m -maximum at extreme points -zero at equilibrium

  8. Mass on a Spring Applet: http://www.walter-fendt.de/ph14e/springpendulum.htm

  9. Position vs Time Graph of Mass on Spring(Sine Curve) x • What is the amplitude? • What is the period? • c) What total distance does the particle travel in one period?

  10. Period of A Spring Mass Oscillator ____ • T=2p√m/k • m mass • k spring constant

  11. Problem • Calculate the period of a mass of 5kg on a spring that has a spring constant of 20N/m. • Answer: 3s

  12. Question • If you had a spring-mass system on the moon, would the period be the same or different than that of this system on the earth?

  13. Harmonic Motion of a Pendulum • Applets: • http://www.walter-fendt.de/ph14e/pendulum.htm • http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true L

  14. Harmonic Motion of a Pendulum • http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true • Period ___ T=2p√L/g g=10m/s2 L=length of string L

  15. Problem • Calculate the Period of a pendulum of length 0.75 m.Answer: 1.7s

  16. Question • If you had a pendulum on the moon would its period be the same or different compared to the same pendulum on the earth?

  17. Questions • Does the period of a pendulum depend on the mass of the bob? • If you increase the length of the pendulum string, what happens to the period?

  18. Calculating k from a F vs x Graph k is the slope of a F vs x graph

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