1. PA114 Waves and Quanta · Unit 1: Oscillations PA114 Waves and Quanta Unit 1: Oscillations and Oscillators (Introduction) Tipler, Chapter 14 www.astro.le.ac.uk/~rda5/PA1140 Dr Richard Alexander (G44B)

2. PA114 Waves and Quanta · Unit 1: Oscillations Mass on a spring Pendulum Atomic bond Oscillators Quartz crystal Tuning fork Tuning circuit

3. PA114 Waves and Quanta · Unit 1: Oscillations Introductory lecture - Simple harmonic motion (SHM) - Angular frequency, phase, and amplitude - Energy in SHM - Damping, forcing - Resonance

4. PA114 Waves and Quanta · Unit 1: Oscillations E x 0 h Anharmonic oscillator U = mgh Total Energy E = K + U

5. PA114 Waves and Quanta · Unit 1: Oscillations Restoring force: Whether the spring is stretched or compressed, the restoring force acts towards the equilibrium position and is linearly related to the displacement (Hooke's Law): Simple Harmonic Motion 0 x > 0 x < 0 x-direction Displacement spring constant Harmonic oscillator

6. PA114 Waves and Quanta · Unit 1: Oscillations T

7. T A - amplitude (maximum displacement) T  - natural period (duration of cycle) f  - frequency (no. of cycles per second or Hz)    - angular frequency (no. of radians per second)

8. PA114 Waves and Quanta · Unit 1: Oscillations T A - amplitude (maximum displacement) T  - natural period (duration of cycle) f  - frequency (no. of cycles per second or Hz)    - angular frequency (no. of radians per second)

9. PA114 Waves and Quanta · Unit 1: Oscillations T A - amplitude (maximum displacement) T  - natural period (duration of cycle) f  - frequency (no. of cycles per second or Hz)    - angular frequency (no. of radians per second)

10. PA114 Waves and Quanta · Unit 1: Oscillations T A - amplitude (maximum displacement) T  - natural period (duration of cycle) f  - frequency (no. of cycles per second or Hz)    - angular frequency (no. of radians per second)

11. PA114 Waves and Quanta · Unit 1: Oscillations T

12. Newton’s 2nd Law: Solution: Parameters: A - unconstrained,  - unconstrained

13. PA114 Waves and Quanta · Unit 1: Oscillations Displacement Initial phase Phase SHM and circular motion

14. PA114 Waves and Quanta · Unit 1: Oscillations What is the energy in the system? Energy is put into the system by the initial compression or stretching of the spring (work done = potential energy) The system also has kinetic energy associated with the motion of the mass

15. PA114 Waves and Quanta · Unit 1: Oscillations K.E. = 1/2 mv 2 E x P.E. = 1/2 kx 2 T.E. = 1/2 kA 2 A 0 stretch compress

16. PA114 Waves and Quanta · Unit 1: Oscillations E x P.E. = 1/2 kx 2 T.E. = 1/2 kA 2 A 0 stretch compress Period the sameVelocities lower

17. PA114 Waves and Quanta · Unit 1: Oscillations Physics is about looking for patterns

18. PA114 Waves and Quanta · Unit 1: Oscillations Mass on a spring Pendulum Atomic bond Oscillators Quartz crystal Tuning fork Tuning circuit

19. PA114 Waves and Quanta · Unit 1: Oscillations Oscillators store energy - like a battery or reservoir Oscillators measure time - unlike a battery or reservoir

20. PA114 Waves and Quanta · Unit 1: Oscillations T.E. explains temperature, thermal expansion, melting,...

21. PA114 Waves and Quanta · Unit 1: Oscillations Damped SHM v friction frictional force: -v damping constant

22. PA114 Waves and Quanta · Unit 1: Oscillations Damped SHM

23. PA114 Waves and Quanta · Unit 1: Oscillations Forced, damped SHM: Resonance

24. PA114 Waves and Quanta · Unit 1: Oscillations Tidal resonance Forced, damped SHM: Resonance

25. PA114 Waves and Quanta · Unit 1: Oscillations Orbital resonance Forced, damped SHM: Resonance

26. PA114 Waves and Quanta · Unit 1: Oscillations Forced, damped SHM driving frequency Oscillations at driving frequency,  ; amplitude depends on how close  is to  0.

27. PA114 Waves and Quanta · Unit 1: Oscillations

28. Coupled oscillators