1. Waves and Quanta PA114 Unit 1: Oscillations and Oscillators
(Introduction)
Tipler, Chapter 14
Dr Richard Alexander (G44B)

2. Oscillators Pendulum Mass on a spring Tuning circuit Atomic bond
fork
Quartz crystal

3. Introductory lecture - Simple harmonic motion (SHM)
- Angular frequency, phase, and amplitude
- Energy in SHM
- Damping, forcing
- Resonance

4. Anharmonic
oscillator E
U = mgh
Total Energy
E = K + U h x

5. Simple Harmonic Motion
oscillator
Displacement
x-direction
spring
constant
x < 0
x > 0
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

6. T

7. A - amplitude (maximum displacement)
T0 - natural period (duration of cycle)
f0 - frequency (no. of cycles per second or Hz)
w0 - angular frequency
(no. of radians per second) T

8. A - amplitude (maximum displacement)
T0 - natural period (duration of cycle)
f0 - frequency (no. of cycles per second or Hz)
w0 - angular frequency
(no. of radians per second) T

9. A - amplitude (maximum displacement)
T0 - natural period (duration of cycle)
f0 - frequency (no. of cycles per second or Hz)
w0 - angular frequency
(no. of radians per second) T

10. A - amplitude (maximum displacement)
T0 - natural period (duration of cycle)
f0 - frequency (no. of cycles per second or Hz)
w0 - angular frequency
(no. of radians per second) T

11. T

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

13. SHM and circular motion
Displacement
Initial phase
Phase

14. 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. E
P.E. = 1/2 kx2
T.E. = 1/2 kA2 A
K.E. = 1/2 mv2 x
stretch
compress

16. E x Period the same Velocities lower A P.E. = 1/2 kx2 T.E. = 1/2 kA2
stretch
compress

17. Physics is about looking for patterns

18. Oscillators Pendulum Mass on a spring Tuning circuit Atomic bond
fork
Quartz crystal

19. Oscillators store energy
- like a battery or reservoir
Oscillators measure time
- unlike a battery or reservoir

20. explains temperature, thermal expansion, melting, ...
Atomic bonds are
“springy”
T.E.
explains temperature, thermal expansion, melting, ...

21. Damped SHM v
friction
frictional force: -v
damping
constant

22. Damped SHM

23. Forced, damped SHM:
Resonance

24. Forced, damped SHM:
Resonance
Tidal resonance

25. Forced, damped SHM:
Resonance
Orbital
resonance

26. Forced,
damped SHM
driving
frequency
Oscillations at driving frequency, w ; amplitude depends on how close w is to w0.

28. Coupled oscillators