1. Damped Oscillations

2. Forced oscillator with damping
resistance force is proportional to speed :
Equation of motion

3. For convenience:
Also, k=mw02
In ‘complex’ method

4. Solution of damped harmonic motion
Define

7. Maximum amplitude at

8. or

9. -q SB

10. Damped oscillation movie
© Walter Fendt (2006)

11. Average energy of the oscillator

13. Plot of r2 vs w (near resonance)

14. Work done by the force per second  Power

15. Stored Energy

16. Mean power

17. Mean stored energy

18. Efficiency of the oscillator
Stored energy in oscillator
Work done by force per cycle

19. Another measure of response
Q factor

20. Summary Damped forced oscillation
Effect of damping is negligible at low and high frequency regime
Effect of damping is large near resonance
Increase in width and shift in resonance frequency with
an increase in damping