Chapter 1 Simple Harmonic Motion 1

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Waves & Oscillations UNIT-I Prepared by Dr B.Lakshmana rao Lecturer in physics V.S.R. GOVT. DEGREE & P.G. COLLEGE, MOVVA Chapter 1 Simple Harmonic Motion 1. Fundamental Definitions 2. Simple Harmonic Motion 3. Application to Sound 4. Damped and Driven Oscillations 5. Combinations of SHM Fundamental Definitions • Position, length, or distance (x or y) • Time (t) • Velocity or speed (v) • Acceleration (a) • Mass (m) • Force (F) • Pressure (p) • Density (ρ) Simple Harmonic Motion • Position x vs. time t • Definition of period T • Definition of amplitude A SHM Systems Simple Harmonic Motion is the projection of Uniform Circular Motion Frequency and Period f = 1/T or T = 1/f or f T =1 T period, in seconds (s) f = frequency in Hertz (Hz) Metric prefixes: centi- (c), milli- (m), micro- ( kilo- (k), mega- (M) Calculations !! Frequency range of human hearing: f = 20 Hz T = 0.05 s = 50 ms f = 20,000 Hz = 20 kHz T = 0.000,05 s = 0.05 ms = 0 s Phase (Time) Phase Difference SHM Position and Velocity Application to Sound Standard complex waves Georg Philipp Telemann (1681-1767): Sonata #1, F-Major, for Recorder and Harpsichord: 1st movement Diego Ortiz Tratado de glosas sobre clausulas y otros generos de puntos en la musica de violones, Roma 1553 Recercada segunda on Doulce Memoire for bass viol, adapted for tenor crumhorn by Richard E. Berg Voice Wave Noise The Psychoacoustic Vibration Transducer Damped and Driven SHM Driven Resonance 1. Vibrating system with natural frequency f0 2. Drive system at frequency f0 with proper phase relationship 3. Amplitude increases while period (frequency) remains constant Coupled Resonance Coupled Pendula Bar-Coupled Pendula Spring-Coupled Pendula Coupled Tuning Bars Wilberforce Pendulum Elastic Pendulum Lissajous Figure components in phase Lissajous Figure components out of phase Lissajous Figure x 90o ahead of y Lissajous Figure x 90o behind y Laser Art Show Spirograph Nebula Chaos at Maryland Prof. James Yorke Distinguished University Professor & Director of the Institute for Physical Science and Technology Ouija Windmill.

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