SOLUTIONS 19.2. Chapter Nineteen: Solutions 19.1 Water 19.2 Solutions 19.3 Acids, Bases, and pH.
19.2 Graphs of Harmonic Motion pp. 419 - 422 Mr. Richter.
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Transcript of 19.2 Graphs of Harmonic Motion pp. 419 - 422 Mr. Richter.
![Page 1: 19.2 Graphs of Harmonic Motion pp. 419 - 422 Mr. Richter.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649f145503460f94c2830d/html5/thumbnails/1.jpg)
19.2 Graphs of Harmonic Motionpp. 419 - 422
Mr. Richter
![Page 2: 19.2 Graphs of Harmonic Motion pp. 419 - 422 Mr. Richter.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649f145503460f94c2830d/html5/thumbnails/2.jpg)
Agenda
Warm Up
Review HW
Recap Period and Frequency
Graphs of Harmonic Motion
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Objectives: We Will Be Able To…
Draw and interpret graphs of harmonic motion.
Determine amplitude, period and frequency from a harmonic motion graph.
![Page 4: 19.2 Graphs of Harmonic Motion pp. 419 - 422 Mr. Richter.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649f145503460f94c2830d/html5/thumbnails/4.jpg)
Warm-Up: Recap
A vibrating string moves back and forth 20 times in 8 seconds.
1. Does it take longer than one second for one complete cycle?
2. What is its period?
3. What is its frequency?
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Recap Period and Frequency
![Page 6: 19.2 Graphs of Harmonic Motion pp. 419 - 422 Mr. Richter.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649f145503460f94c2830d/html5/thumbnails/6.jpg)
Period and Frequency
The period (T) of an object’s motion is the time it takes for an object to complete one full cycle of motion. Because period is a measurement of time per cycle, the
units of period (T) are units of time: seconds.
The frequency (ƒ) of an object’s motion the number of cycles the object completes per unit of time.
Frequency is a measure of how many cycles per unit time, so the units of frequency are “per seconds” We abbreviate as Hertz (Hz).
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Period and Frequency
You may have noticed that period and frequency are inverses of each other.
If an object takes 8 seconds to complete 20 cycles: It completes 1 cycle in 8/20 seconds (T = 0.4 seconds) It completes 20/8 cycles per second (ƒ = 2.5 Hz)
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Graphs of Harmonic Motion
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Graphs of Harmonic Motion
An example:
Let’s say there is a pendulum that takes 4 seconds to complete a cycle, and it oscillates back and forth from –10 cm to 10 cm.
What does that graph look like? Let’s plot some points.
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Graphs of Harmonic Motion
10
-10
Time (s)
1 2 3 4 5 6 7 8
Dis
pla
cem
ent
(cm
)
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Graphs of Harmonic Motion: Amplitude
10
-10
Time (s)
1 2 3 4 5 6 7 8
Dis
pla
cem
ent
(cm
)
Amplitude = 10 cm
Amplitude = 10 cm
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Graphs of Harmonic Motion: Period
10
-10
Time (s)
1 2 3 4 5 6 7 8
Dis
pla
cem
ent
(cm
)
T = 4 seconds
T = 4 seconds
T = 4 seconds
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Graphs of Harmonic Motion: Frequency
10
-10
Time (s)
1 2 3 4 5 6 7 8
Dis
pla
cem
ent
(cm
)
T = 4 seconds
T = 4 seconds
T = 4 seconds
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Wrap-Up: Did we meet our objectives?
Draw and interpret graphs of harmonic motion.
Determine amplitude, period and frequency from a harmonic motion graph.
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Homework
p. 431 Solving Problems
# 1, 2, 4, 6, 7