Transcript Document
Forced Oscillations
Solution=Complementary Function +
Particular Integral
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Solutions
Complementary Functions are transients
Steady State behaviour is decided by the
Particular Integral
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Solution with Damping
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Amplitude and Phase (again)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Amplitude and Phase (again)
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://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
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Average Energy
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Average Energy Plot
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Mild Damping
Maxima at
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Mild Damping
Maxima at
Lorentzian Profile
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
FWHM
FHWM=
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Power
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Average Power
Using
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Average Power
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Mild Damping
Lorentzian Profile
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/
Average Power
Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India
http://www.cts.iitkgp.ernet.in/~phy1/