Measuring Harmonic Motion. Amplitude Maximum displacement from the equilibrium position.
Measuring Simple Harmonic Motion Chapter 12 Section 2.
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Transcript of Measuring Simple Harmonic Motion Chapter 12 Section 2.
![Page 1: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/1.jpg)
Measuring Simple Harmonic Motion
Chapter 12 Section 2
![Page 2: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/2.jpg)
Measuring The Motion
There are 3 things that determine the motion of a mass in simple harmonic motion. Amplitude Period Frequency
![Page 3: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/3.jpg)
Amplitude
Amplitude – The maximum displacement from the equilibrium position.
Can be measured in different ways Pendulum – The angle (radians) between the
equilibrium position and the maximum displacement.
Spring-mass – The maximum amount (meters) stretched or compressed from the equilibrium position.
![Page 4: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/4.jpg)
Period
Period – The time it takes to execute a complete cycle of motion.
For example: If it takes 5 seconds for a person on a swing to
swing back and forth, then the period of the motion would be 5 seconds.
SI units for period – Seconds (s) Variable given for period – Capital letter (T)
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Displacement For Period
The displacement of an object in simple harmonic motion during the time of 1T (time to compete one cycle) is “ZERO.”
![Page 6: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/6.jpg)
Frequency
Frequency – The number of cycles or vibrations per unit time.
For example: The person on the swing completes one cycle in 5
seconds, the frequency would be 1/5 cycles per second or 0.2 cycles per second.
![Page 7: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/7.jpg)
Units For Frequency
SI units for frequency – S-1
This is known as Hertz (Hz) Variable for frequency – lower case letter (f) In the case of the person swinging, the
frequency would be: 0.2 cycles per second = 0.2 Hz
A typical TV set has a frequency of 60Hz, which means 60 frames per second.
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Differences Between Period and Frequency
Period is time per cycle. Frequency is the number of cycles per unit
time. They are inversely proportional.
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Equations For Frequency and Period
If the period or the frequency is known, this relationship can be used to calculate the other value. Period (s) Frequency (Hz)
![Page 10: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/10.jpg)
Determining The Period of a Pendulum
The strings length and the free fall acceleration determine the period of a simple pendulum.
Things that don’t determine the Period: Amplitude (for angles less then 15 degrees) Mass of the bob
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Simple Pendulum Equation
![Page 12: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/12.jpg)
Example Problem #1
A desktop toy swings back and forth once every 1.0 seconds. How tall is this toy?
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Example Problem #1 Answer
length = 0.25m
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Example Problem #2
What is the period of a 3.98m long pendulum?
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Example Problem #2 Answer
T = 4.00 seconds
![Page 16: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/16.jpg)
Period of a Mass-Spring System
The mass attached to the spring and the spring constant (k) determine the period.
Things that don’t determine the period: Amplitude
![Page 17: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/17.jpg)
Period of a Mass-Spring System Equation
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Example Problem #3
A 1.0 kg mass attached to one end of a spring completes one oscillation every 2.0 seconds. Find the spring constant.
![Page 19: Measuring Simple Harmonic Motion Chapter 12 Section 2.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a97aae/html5/thumbnails/19.jpg)
Example Problem #3 Answer
k = 9.9N/m