1. Damped Oscillations 1

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

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

4. Solution of damped harmonic motion
Define 4

5. 5

6. 6

7. Maximum amplitude at 7

8. or

9. -q SB 8

10. Average energy of the oscillator9

11. 10

12. Plot of r2 vs w (near resonance)11

13. Work done by the force per second  Power12

14. Stored Energy 13

15. Mean power 14

16. Mean stored energy 15

17. Efficiency of the oscillator
Stored energy in oscillator
Work done by force per cycle 16

18. Another measure of response
Q factor

19. Pohl’s Pendulum
Forced and Damped Oscillation 17

20. 1. Stimulation motor 2. Rotating pendulum 3. Bearing block
4. Electromagnetic break 5. Spiral spring 18

21. If a large conductive metal plate is moved through a
Eddy current brake
If a large conductive metal plate is moved through a
magnetic field which intersects perpendicularly to the sheet,
the magnetic field will induce small "rings" of current
which will actually create internal magnetic fields opposing
the change. This is why a large sheet of
metal swung through a strong magnetic field will stop as
it starts to move through the field. 19

22. Eddy current 20

23. Find frequency of oscillations with different damping current
Check: the frequency of oscillation should decrease with
increase in damping current.
2. In a semi log plot Check whether amplitude decreases
logarithmically with time
3. Check whether the maximum of resonance curve shifts
towards lower frequency with increasing in damping.
4. Check whether the width of the resonance curve is more with
higher damping current
5. Check the phase difference between the exciter and pendulum
--- much above resonance and much below the resonance.
Pohl’s Pendulum: Compare model SHO and Experiment 21

24. 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

25. Reference FEYNMAN LECTURES ON PHYSICS VOL I
Author : RICHARD P FEYNMAN,
IIT KGP Central Library :
Class no.  530.4