forced oscillations
DESCRIPTION
Forced Oscillations. Solution= Complementary Function + Particular Integral. Solutions. Complementary Functions are transients. Steady State behaviour is decided by the Particular Integral. Solution with Damping. Amplitude and Phase (again). Amplitude and Phase (again). -. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/1.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Forced Oscillations
Solution=Complementary Function +Particular Integral
![Page 2: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/2.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Solutions
Complementary Functions are transients
Steady State behaviour is decided by theParticular Integral
![Page 3: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/3.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Solution with Damping
![Page 4: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/4.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Amplitude and Phase (again)
![Page 5: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/5.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Amplitude and Phase (again)
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![Page 6: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/6.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Some Key Points
High frequency and low frequency behaviour unchanged by damping
Amplitude is finite throughout
Maximum Amplitude at
![Page 7: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/7.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/ Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Average Energy
![Page 8: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/8.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Average Energy Plot
![Page 9: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/9.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Mild Damping
Maxima at
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Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Mild Damping
Maxima at
Lorentzian Profile
![Page 11: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/11.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
FWHM
FHWM=
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Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Power
![Page 13: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/13.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Average Power
Using
![Page 14: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/14.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Average Power
![Page 15: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/15.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Mild Damping
Lorentzian Profile
![Page 16: Forced Oscillations](https://reader033.vdocument.in/reader033/viewer/2022061517/56814dd3550346895dbb3435/html5/thumbnails/16.jpg)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/
Average Power