1. February 23, 2016Introduction1 Oscillations

2. February 23, 2016Introduction2 Examples Obvious Oscillations » pendulums » car springs, shock absorbers » water waves » earthquakes Less-Obvious Oscillations » musical instruments - guitar, piano, flute » suspension bridges » lasers » quartz-crystal electronic watches » radio antennae » fiber optics

3. February 23, 2016Introduction3 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…” Oscillations

4. February 23, 2016Introduction4 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”

5. 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

6. February 23, 2016Introduction6 Similarly….. “Waves are everywhere” Mechanical waves (sound, water, phonons…) Electromagnetic waves (radiation, visible light…) Matter waves (atoms) Gravitational waves (neutron stars, black holes..)

7. February 23, 2016Introduction7 OSCILLATIONS Harmonic Oscillation Known Examples

8. February 23, 2016Introduction8

9. February 23, 2016Introduction9 Hooke’s Law: SHM Angular frequency Time period

10. February 23, 2016Introduction10

11. February 23, 2016Introduction11 Torsional Oscillation

12. February 23, 2016Introduction12

13. February 23, 2016Introduction13 Solution: A=Amplitude A=2 units = Initial Phase

14. 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