1. Lab 2: Simple Harmonic Oscillators – Resonance & Damped Oscillations
Non-Harmonic Oscillators
Harmonic Oscillators
Spring Constant
Measuring Period for Different Amplitudes
Changing Mass and Restoring Force
Changing the Spring Constant
Resonance and Damped Oscillations
Damped Oscillations
Effect of Damping
Resonance Curve
Buildup Time of Oscillation

2. Simple Harmonic Motion
periodic sinusoidal motion,
f and A are independent of each other.
Oscillation amplitude will
Damp out without a driving force due to internal friction.
Build (add) up when driving frequency fD is close to resonant frequency fR.
Stay small when fD is away from fR. Dm

3. Damped Oscillations t A You can find T (= 1/fN ) and t from this graph
equilibrium
You can find T (= 1/fN ) and t from this graph
Natural frequency (fN) : The frequency of oscillation in the absence of an external driving force
Damping time (t) : The time it takes for the amplitude to decrease by a factor of 2

4. Resonance Curve A plot of oscillation A versus fD Df
f f2
Df : Width of the resonance curve at half-maximum height (FWHM)

5. Relationship between  and f
Df : resonance width of resonance curve (continuously driven oscillation)
t : damping time of damped oscillation (naturally decaying oscillation)
Check if the relationship works for your experiments!

6. Lab 2: Sample Data – Damped Oscillation
Unit B

7. Lab 2: Measuring TN
Unit B

8. Lab 2: Measuring A to find 
Unit B

9. Lab 2: Measuring 
Unit B

10. Creating Resonance Curve
Estimate the resonance frequency fR first
It’s the peak frequency!
Measure the oscillation amplitude A at various driving frequency fD
Use the range fR ± 2 Hz
Take finer steps near fR (i.e Hz)
Note: Turn the frequency knob in only one direction (i.e. increasing f direction)
Then make a resonance curve plot

11. Lab 2: fD = fR = Hz
Unit B

12. Lab 2: fD = 8.61 Hz
Unit B

13. Lab 2: fD = 8.61 Hz
Unit B

14. Lab 2: fD = 8.61 Hz
Unit B

15. Lab 2: fD = 8.61 Hz
Unit B

16. Lab 2: fD = 9.61 Hz
Unit B

17. Lab 2: fD = 9.61 Hz
Unit B

18. Lab 2: fD = 9.61 Hz
Unit B

19. Lab 2: fD = Hz
Unit B

20. Lab 2: fD = Hz
Unit B

21. Lab 2: fD = Hz
Unit B

22. Lab 2: fD = Hz
Unit B

23. To determine Df easily, graph data points within ±0.5 Hz range of fR

24. Example Resonance Curve
continue plotting all data sets

25. Df = f2 – f1 fR
Draw a smooth curve that fits to all data points the best – don't connect points! Df
f f2

26. Lab 2: Driving f = 10.61 Hz Buildup Time w/Magnet Far
Unit B

27. Lab 2: Driving f = 10.61 Hz Buildup Time w/Magnet Far
Unit B

28. Lab 2: Driving f = 10.61 Hz Buildup Time w/Magnet Near
Unit B

29. Lab 2: Driving f = 10.61 Hz Buildup Time w/Magnet Near
Unit B

30. Lab 2: Driving f = 10.61 Hz Buildup Time w/o Magnet
Unit B