February 23, 2016Introduction1 Lets begin...CHAPTER1
February 23, 2016Introduction2 Oscillations in nature are ubiquitous (found everywhere) Some oscillations are visible; some are subtle but it is difficult to find something which never exhibits oscillations. Examples: – A mosquito’s wings, for example, vibrate hundreds of times per second and produce an audible note. – The whole earth, after being jolted by an earthquake, may continue to vibrate at the rate of about one oscillation per hour. – The human body itself is a treasure-house of vibratory phenomena. “After all, our hearts beat, our lungs oscillate, we can hear and speak because our eardrums and larynges vibrate. The light waves which permit us to see entail vibration. We move by oscillating our legs, even the atoms of which we are constituted vibrate…” Chapter 1: Oscillations
February 23, 2016Introduction3 As a result… ¤ They have an enormous impact on understanding how things work. ¤ In thermal physics, quantum mechanics, optics, condensed-matter physics, mechanics, atmospheric and planetary physics, astrophysics, etc. “So it’s a basic literacy in physics”
February 23, 2016Introduction4 Examples Obvious Oscillations » water waves » pendulums » earthquakes » car springs, shock absorbers Less-Obvious Oscillations » musical instruments - guitar, piano, flute » suspension bridges » lasers » quartz-crystal electronic watches » radio antennae » fiber optics
February 23, 2016Introduction5 Subtle Oscillations » heat in a solid » structure of an atom » superconductivity » heat radiation » ozone protection » rings of Saturn » quantum mechanical zero-point energy More examples
February 23, 2016Introduction6 Similarly….. “Waves are everywhere” Mechanical waves (sound, water, phonons…) Mechanical waves (sound, water, phonons…) Electromagnetic waves (radiation, visible light…) Electromagnetic waves (radiation, visible light…) Matter waves (atoms) Matter waves (atoms) Gravitational waves (neutron stars, black holes..) Gravitational waves (neutron stars, black holes..)
February 23, 2016Introduction7 OSCILLATIONS Harmonic Oscillation: Known Examples
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February 23, 2016Introduction9 Hooke’s Law: SHM Angular frequency Time period
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February 23, 2016Introduction11 Torsional Oscillation
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February 23, 2016Introduction13 Solution: A=Amplitude, A=2 units =Phase
February 23, 2016Introduction14 Solutions: Requirements » sine- cosine form of solutions » To introduce exponential form of solutions » To be familiar with the solution of differential equations