1. PHYSICS 1 External Forcing Why this particular type of force?
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, India

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