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

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

Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/

Solution with Damping

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)

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)

-

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

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

Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/

Average Energy Plot

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

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

Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/

FWHM

FHWM=

Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/

Power

Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/

Average Power

Using

Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/

Average Power

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

Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 Indiahttp://www.cts.iitkgp.ernet.in/~phy1/

Average Power