Foundations of Physical Science Unit 4: Sounds and Waves

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

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.

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

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

11.1 Harmonic Motion

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)

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

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

Harmonic Motion In… nature technology art and music

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

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)

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

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

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

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)

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

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

11.2 Graphs of Harmonic Motion

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

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

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

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

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

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!

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

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!

11.3 Simple Mechanical Oscillators

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