1. Forced Oscillations Damped
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Forced Vibration- Damped Case

2. F(t) : general time dependent
External Force is
F(t) : general time dependent
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Forced Vibration- Damped Case

3. Forced Vibration- Damped Case
Forced oscillator:Damped case
Time dependent function
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Forced Vibration- Damped Case

4. Forced Vibration- Damped Case
Companion equation:
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Forced Vibration- Damped Case

5. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

6. Forced Vibration- Damped Case
Complementary function:
Transients
Try steady state solution (Particular solution)
Find
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Forced Vibration- Damped Case

7. Forced Vibration- Damped Case
Complementary function:
Transients
Try steady state solution (Particular solution)
Find
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Forced Vibration- Damped Case

8. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

9. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

10. Forced Vibration- Damped Case
Amplitude:
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Forced Vibration- Damped Case

11. Forced Vibration- Damped Case
Phase:
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Forced Vibration- Damped Case

12. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

13. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

14. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

15. Forced Vibration- Damped Case
Show amplitude resonance at:
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Forced Vibration- Damped Case

16. Forced Vibration- Damped Case
Forced oscillations for different resistances
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Forced Vibration- Damped Case

17. Forced Vibration- Damped Case
Amplitude and phase
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Forced Vibration- Damped Case

18. Forced Vibration- Damped Case
Different driving amplitudes
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Forced Vibration- Damped Case

19. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

20. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

21. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

22. Forced Vibration- Damped Case
Instantaneous power absorbed by the system:
Average power over one cycle:
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Forced Vibration- Damped Case

23. Forced Vibration- Damped Case
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Forced Vibration- Damped Case

24. Forced Vibration- Damped Case
Peak Power:
Width at half peak power =
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Forced Vibration- Damped Case

25. Forced Vibration- Damped Case
Averaged power absorbed = < P >
/ 2
= 3
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Forced Vibration- Damped Case

26. Forced Vibration- Damped Case
Stored energy:
Problem: What is the peak value
and for what driving frequency?
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Forced Vibration- Damped Case

27. Forced Vibration- Damped Case
Stored energy: < E >
= 3
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Forced Vibration- Damped Case

28. Forced Vibration- Damped Case
Resonant quality factor:
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Forced Vibration- Damped Case

29. F(t) : Sin(wt) or Cos(wt)
External Force is
F(t) : Sin(wt) or Cos(wt)
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Forced Vibration- Damped Case

30. Forced Oscillations Solution=Complementary Function +
Particular Integral

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

32. Solution with Damping

33. Amplitude and Phase (again)

34. Amplitude and Phase (again)-

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

36. Average Energy
PHYSICS 1

37. Average Energy Plot

38. Mild Damping
Maxima at

39. Mild Damping
Maxima at

40. FWHM
FHWM=

41. Power

42. Average Power
Using

43. Average POwer

44. Lorentzian Profile