Transcription of Chapter 15 Oscillations and Waves
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Chapter 15 Oscillations and Waves
Chapter 15 Oscillations and WavesMFMcGraw-PHY 2425 Chap 15Ha- Oscillations -Revised 10/13/20122 Oscillations and Waves Simple Harmonic Motion Energy in SHM Some Oscillating Systems Damped Oscillations Driven Oscillations ResonanceMFMcGraw-PHY 2425 Chap 15Ha- Oscillations -Revised 10/13/20123 Simple Harmonic MotionSimple harmonic motion (SHM) occurs when the restoring force (the force directed toward a stable equilibrium point) is proportional to the displacement from 2425 Chap 15Ha- Oscillations -Revised 10/13/20124 Characteristics 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 2425 Chap 15Ha- Oscillations -Revised 10/13/20125A Simple harmonic oscillator (SHO)Frictionless surfaceThe restoring force is F = 2425 Chap 15Ha- Oscillations -Revised 10/13/20126 Frictionless surfaceTwo Springs with Different AmplitudesMFMcGraw-PHY 2425 Chap 15Ha- Oscillations -Revised 10/13/20127 SHO Period is Independent of the AmplitudeMFMcGraw-PHY 2425 Chap 15Ha- Oscillations -Revised 10/13/20128 The period of oscillation =Twhere is the angular frequency of the Oscillations , k is the spring constant and m is the mass of the The Period and the Angular FrequencyMFMcGraw-PHY 2
A simple harmonic oscillator can be described mathematically by: ( ) ( ) ( ) 2 x t = Acos ωt dx v t = = -A ωsin ωt dt dv a t = = -A ωcos ωt dt Or by: ( ) ( ) ( ) 2 x t = Asin ωt dx v t = = A ωcos ωt dt dv a t = = -A ωsin ωt dt where A is the amplitude of the motion, the maximum displacement from equilibrium, A ω = v max, and Aω2 = a ...
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