1. UMBC – Physics Department Prof. J
UMBC – Physics Department Prof. J. Vanderlei Martins PHYS 224 – Oscillations and Waves Additional Material Showed in Class:

2. Ae-(b/2m) t Adapted from:

3. Over Damping Critical Damping Under Damping No Damping Adapted from:

4. Coupled Oscillators and Normal Modes :

5. Superposition of normal modes of oscillation with different amplitudes can produce very complex oscillation patterns:
This Example shows 8 normal modes of oscillation that where excited in a given string with different amplitudes
Credit:

6. Normal Modes of a String in a particular pattern of wave motion:
First eight contributing normal modes of string with fixed ends.
This is equivalent to two identical traveling waves moving in opposite directions.
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7. Normal Modes of a String in a particular pattern of wave motion:
First eight contributing normal modes of string with fixed ends.
This is equivalent to two identical traveling waves moving in opposite directions.
Partial Sum of the 8 most important normal mode contributions:
Credit:

8. Interacting Pulses

9. Interacting Pulses – same direction