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External Forcing

Understand the impact of an additional external force in physics through Fourier Series analysis. Discover the solutions for single and multiple frequencies, emphasizing the importance of damping effects in controlling system behavior. Learn about stiffness and mass-controlled regimes and the decisive role of particular integrals. Gain insight into amplitude and phase responses in varying frequency ranges.

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External Forcing

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  1. External Forcing SHO with an additional external force PHYSICS 1 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/

  2. Fourier Series For any arbitrary time varying force

  3. Solution using Fourier Series Find solution for a single frequency Superpose solutions

  4. The equation where Solution=Complementary Function + Particular Integral

  5. Particular Integral

  6. Amplitude and Phase

  7. Amplitude and Phase

  8. Low Frequency Response Stiffness Controlled Regime

  9. High Frequency Response Mass Controlled Regime solution of

  10. Effect of Damping Solution=Complementary Function + Particular Integral

  11. Solutions Complementary Functions are transients Steady State behaviour is decided by the Particular Integral

  12. Solution with Damping

  13. Amplitude and Phase (again)

  14. Amplitude and Phase (again) -

  15. Some Key Points High frequency and low frequency behaviour unchanged by damping Amplitude is finite throughout Maximum Amplitude at

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