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Simple Harmonic Motion

YouTube - Color Footage of Tacoma Narrows YouTube - Tacoma Narrows Bridge Collapse "Gallopin' Gertie". Simple Harmonic Motion. Periodic Motion. Motion reoccurs in a regular pattern

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Simple Harmonic Motion

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  1. YouTube - Color Footage of Tacoma Narrows YouTube - Tacoma Narrows Bridge Collapse "Gallopin' Gertie" Simple Harmonic Motion

  2. Periodic Motion • Motion reoccurs in a regular pattern • Simple harmonic motion (SHM): force that restores the object to equilibrium is directly proportional to the displacement • Two important measurements: • Period (T): time to repeat one complete cycle • Amplitude: maximum displacement

  3. Mass on a Spring • Hooke's Law: force exerted by a spring is directly proportional to the amount the spring is stretched • F = -kx • PE=(1/2)kx2 • http://web.hep.uiuc.edu/home/mats/WCIA/wcia_030430_1.wmv

  4. Springs! • Masses & Springs 2.02

  5. Example • A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from the end. What is the spring constant? • Known: x=0.18m F=56N • F=-kx so k=F/x (the negative just means it's a restoring force)‏ • k=56N/0.18m = 310 N/m

  6. Example Continued • How much PE is stored in the spring? • PE=(1/2)kx2 • PE=(1/2)(310N/m)(0.18m)2 • PE=5 J

  7. Now you try it! • A 560 N bicyclist sits on a bicycle seat and compresses the two springs that hold it up. The spring constant is 2.2 x 104 N/m for each spring. How much is each spring compressed? • Know: F=560 N k=2.2 x 104 N/m 2 springs • F=-kx or x=F/k and since 2 springs x=F/2k • X=1.3 x 10-2 m

  8. Period of a Spring • Mass attached to a spring exhibits simple harmonic motion • T= 2π√(m/k) • Frequency is inverse of period!

  9. Pendulum • Object (bob) suspended by a string of length l • String exerts tension (force) and gravity exerts force • Period of a pendulum: T=2π√(l/g)

  10. Sample Problem • A pendulum with length 36.9 cm has a period of 1.22 s. What is the acceleration of gravity at the pendulum's location? • Known: T=1.22 s l=0.369 m • T=2π√l/g so g=(2π)2l (T)2 • g=9.78 m/s2

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