forced vibrations a system with a driving force will force a vibration at its frequency when the...
TRANSCRIPT
![Page 1: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/1.jpg)
Forced Vibrations
• A system with a driving force will force a vibration at its frequency
• When the frequency of the driving force equals the natural frequency of the system, the system is said to be in resonance
![Page 2: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/2.jpg)
Standing Waves
• When an incident wave interferes with a reflected wave to form areas of constructive and destructive interference.
Nodes are where the resulting wave remains stationary.Anti-nodes are where the resulting wave has max amplitude.
![Page 3: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/3.jpg)
Other Examples of Resonance
• Child being pushed on a swing• Shattering glasses• Tacoma Narrows Bridge collapse due to
oscillations by the wind• Upper deck of the Nimitz Freeway collapse
due to the Loma Prieta earthquake
![Page 4: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/4.jpg)
1989 Loma Prieta earthquakeAka Quake of '89
World Series Earthquake
![Page 5: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/5.jpg)
Resonance
Resonance: a vibration of large amplitude in a mechanical or electrical system caused by a relatively small periodic stimulus of the same or nearly the same period as the natural vibration period of the system.
http://www.merriam-webster.com/dictionary/resonance
![Page 6: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/6.jpg)
How many wavelengths?
1
2
1 ½
½
![Page 7: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/7.jpg)
How does a Guitar String Vibrate?
½ = L
= 2L
L
![Page 8: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/8.jpg)
What is the velocity of the wave on the string?
v = f = 2L
![Page 9: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/9.jpg)
Different Frequencies
• How can I change the frequency (note)?
![Page 10: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/10.jpg)
Harmonics!
• When you sound the guitar note, you hear other frequencies.
![Page 11: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/11.jpg)
How does a Guitar String Vibrate?
![Page 12: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/12.jpg)
How does a Guitar String Vibrate?
![Page 13: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/13.jpg)
How does a Guitar String Vibrate?
![Page 14: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/14.jpg)
Fundamental frequency
2nd Harmonic
3rd Harmonic
4th Harmonic
= 2L
f2 = v/L
f3 = 3v/2L
f4 = 2v/L
f1 = v/2L
= L
= 2/3 L
= ½ L
![Page 15: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/15.jpg)
Summary
f = nv/2L
n is the # of antinodes or harmonic
• Fundamental Frequency is the LOWEST frequency
• All harmonics are multiples of the fundamental frequency (e.g. f1 = 50 hz, then f2 = 100 hz, f3 = 150 hz, etc)
= 2L/n
![Page 16: Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649f055503460f94c1a57c/html5/thumbnails/16.jpg)
Fundamental frequency1st Harmonic
2nd Harmonic
3rd Harmonic
4th Harmonic
How does a Guitar String Vibrate?