Chapter 15 Oscillations and Waves

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Chapter 15Oscillations and WavesMFMcGraw-PHY 2425Chap 15Ha- Oscillations -Revised 10/13/20122Oscillations and Waves Simple Harmonic Motion Energy in SHM Some Oscillating Systems Damped Oscillations Driven Oscillations ResonanceMFMcGraw-PHY 2425Chap 15Ha- Oscillations -Revised 10/13/20123Simple Harmonic MotionSimple harmonic motion (SHM) occurs when the restoring force (the force directed toward a stable equilibrium point) is proportional to the displacement from 2425Chap 15Ha- Oscillations -Revised 10/13/20124Characteristics of SHM Repetitive motion through a central equilibrium point. Symmetry of maximum displacement. Period of each cycle is constant. Force causing the motion is directed toward the equilibrium point (minus sign). F directly proportional to the displacement from = - 2 x DisplacementMFMcGraw-PHY 2425Chap 15Ha- Oscillations -Revised 10/13/20125A Simple Harmonic Oscillator (SHO)Frictionless surfaceThe restoring force is F = 2425Chap 15Ha- Oscillations -Revised 10/13/20126Frictionless surfaceTwo Springs with Different AmplitudesMFMcGraw-PHY 2425Chap 15Ha- Oscillations -Revised 10/13/20127SHO Period is Independent of the AmplitudeMFMcGraw-PHY 2425

Assuming the table is frictionless: ( ) ( ) ( ) ∑ x x 2 x F = - kx = ma k ... The origin is at the pivot point. The coordinates are (r, φ). The r-coordinate points from the origin along the rod. The φ- ... Example: A clock has a pendulum that performs one full swing every 1.0 sec. The object at the end of the string weighs 10.0 N.

  Table, Example, Pivot