Transcript Document
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/