1. Foundations of Physical Science
Unit 4: Sounds and Waves

2. Chapter 11: Harmonic Motion
11.2 Graphs of Harmonic Motion
11.3 Simple Mechanical Oscillators

3. Learning Goals
Learn about harmonic motion and how it is fundamental to understanding natural processes.
Use harmonic motion to keep accurate time using a pendulum.
Learn how to interpret and make graphs of harmonic motion.

4. Learning Goals (continued)
Construct simple oscillators.
Learn how to adjust the frequency and period of simple oscillators.
Learn to identify simple oscillators.

5. Vocabulary amplitude cycle frequency harmonic motion hertz
oscillator phase
period
periodic motion
system

6. 11.1 Harmonic Motion

7. Motion Linear: motion from one place to another
Distance, time, speed, acceleration
Harmonic: motion that repeats itself over and over
HARMONY, which means “multiples of”
Swinging back and forth (pedals on a bicycle)

8. Cycles, Systems, and Oscillators
Cycle: the building block of harmonic motion; a unit of motion that repeats over and over
A cycle has a beginning and an end

9. Cycles, Systems, and Oscillators
System: a group that includes all the things we are interested in studying
Oscillator: a system that shows harmonic motion
ex. pendulum
ex. heart and its muscles

10. Harmonic Motion In…
nature
technology
art and music

11. Investigating Harmonic Motion
Period: the time for one cycle
Measured in seconds (s)
Frequency: the number of cycles per second; the inverse of period
Measured in cycles per second
Measured in hertz

12. Frequency How frequently a vibration occurs
The number of to and fro vibrations the object makes in a given time (usually one second)
Hertz: the unit of frequency
1 vibration per 1 second = 1 hertz (Hz)

13. Period The time it takes for a complete vibration Frequency = 1 period

14. Example
An electric toothbrush completes 90 cycles every second. What is its:
(a) frequency?
(b) period?
(a) 90 cycles/second = 90 vibrations/second = 90 Hz
(b) 1/90 second

15. Example
Gusts of wind cause the Sears building in Chicago to sway back and forth, completing a cycle every 10 seconds. What is its:
(a) frequency?
(b) period?
(a) 1/10 Hz
(b) 10 seconds

17. Amplitude The size of a cycle
Measured in units appropriate to the kind of oscillation you are describing
Maximum distance the motion moves away from the average (for a pendulum this is the center)

18. Amplitude
The distance from the midpoint to the crest (or trough) of the wave
Equals the maximum displacement from the home position-from equilibrium

19. Amplitude
Damping: the gradual loss of amplitude of an oscillator (such as a pendulum), usually due to friction

20. 11.2 Graphs of Harmonic Motion

21. Graphs of Motion Linear motion graphs show one direction
Harmonic motion graphs show cycles
Period and amplitude can be read from the graphs
If you know period and amplitude you can sketch the harmonic graph

22. Reading Harmonic Motion Graphs
Most show how things change with time
Use positive and negative values to represent motion on either side of the center
Zero is the equilibrium point

23. Reading Harmonic Motion Graphs
The example graph shows a pendulum swinging from +20 cm to -20 cm and back
The amplitude is the maximum distance from the center, or 20 cm

24. Determining Amplitude from the Graph
Amplitude: half the distance between the highest and lowest points on the graph
The difference is called the peak-to-peak value

25. Determining Period from the Graph
Period: time difference between the beginning of the cycle and the end

26. Circles and Harmonic Motion
Circular motion: similar to harmonic motion; always has a cycle of 360 degrees
The phase of an oscillator: where is a pendulum 1/10th through its cycle? If we let a cycle be 360 degrees, then 1/10th is 36 degrees!

27. Circles and Harmonic Motion
“In Phase”: two oscillators that have cycles aligned

28. Circles and Harmonic Motion
“Out of Phase”: two oscillators that have cycles out of alignment
by 90 (1/4th a cycle)
or 180 degrees (1/2 a cycle)
or any other degree!

29. 11.3 Simple Mechanical Oscillators

30. Simple Mechanical Oscillators
Pendulums
Masses on springs
Vibrating strings on musical instruments