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Simple Harmonic Motion (SHM)

Simple Harmonic Motion (SHM). (and waves). What do you think Simple Harmonic Motion (SHM) is???. Defining SHM. Equilibrium position Restoring force Proportional to displacement Period of Motion Motion is back & forth over same path. Θ. F g. Describing SHM. Amplitude. Θ. F g.

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Simple Harmonic Motion (SHM)

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  1. Simple Harmonic Motion (SHM) (and waves)

  2. What do you think Simple Harmonic Motion (SHM) is???

  3. Defining SHM • Equilibrium position • Restoring force • Proportional to displacement • Period of Motion • Motion is back & forth over same path

  4. Θ Fg Describing SHM • Amplitude

  5. Θ Fg Describing SHM • Period (T) • Full swing • Return to original position

  6. Frequency • Frequency- Number of times a SHM cycles in one second (Hertz = cycles/sec) • f = 1/T

  7. SHM Descriptors • Amplitude (A) • Distance from start (0) • Period (T) • Time for complete swing or oscillation • Frequency (f) • # of oscillations per second

  8. Oscillations • SHM is exhibited by simple harmonic oscillators (SHO) • Examples?

  9. Examples of SHOs • Mass hanging from spring, mass driven by spring, pendulum

  10. SHM for a Pendulum • T = period of motion (seconds) • L = length of pendulum • g = 9.8 m/s2

  11. SHM Quantities

  12. Energy in SHO

  13. Energy in SHO

  14. EPE = ½ k x2 • KE = ½ m v2 • E = ½ m v2 + ½ k x2 • E = ½ m (0)2 + ½ k A2E = ½ k A2 • E = ½ m vo2 + ½ k (0)2E = ½ m vo2

  15. √ Velocity • E = ½ m v2 + ½ k x2 • ½ m v2 + ½ k x2 = ½ k A2 • v2 = (k / m)(A2 - x2) = (k / m) A2 (1 - x2 / A2) • ½ m vo2 = ½ k A2 • vo2 = (k / m) A2 • v2 = vo2 (1 - x2 / A2) • v = vo 1 - x2 / A2

  16. Damped Harmonic Motion • due to air resistance and internal friction • energy is not lost but converted into thermal energy

  17. Damping • A: overdamped • B: critically damped • C: underdamped

  18. Resonance • occurs when the frequency of an applied force approaches the natural frequency of an object and the damping is small (A) • results in a dramatic increase in amplitude

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