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External Forcing SHO with an additional external force Why this particular type of force? Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India http://www.cts.iitkgp.ernet.in/~phy1/ Fourier Series For any arbitrary time varying force Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India http://www.cts.iitkgp.ernet.in/~phy1/ Solution using Fourier Series Find solution for a single frequency Superpose solutions Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India http://www.cts.iitkgp.ernet.in/~phy1/ The equation where 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/ Particular Integral 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 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 Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India http://www.cts.iitkgp.ernet.in/~phy1/ Low Frequency Response Stiffness Controlled Regime Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India http://www.cts.iitkgp.ernet.in/~phy1/ High Frequency Response Mass Controlled Regime solution of Somnath Bharadwaj and Pratik Khastgir, Department of Physics and Meteorology, IIT Kharagpur, 721 302 India http://www.cts.iitkgp.ernet.in/~phy1/ Effect of Damping 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/