Title: UMBC
1UMBC Physics Department Prof. J. Vanderlei
MartinsPHYS 224 Oscillations and
WavesAdditional Material Showed in Class
2Ae-(b/2m) t
Adapted from http//webphysics.davidson.edu/physl
et_resources/bu_semester1/c19_damped_sim.html
3Over Damping
Critical Damping
Under Damping
No Damping
Adapted from http//webphysics.davidson.edu/physl
et_resources/bu_semester1/c19_damped_sim.html
4Coupled Oscillators and Normal Modes
5Superposition 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 http//www.calpoly.edu/gepstein/NormalMod
es/
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.
Credit http//www.calpoly.edu/gepstein/NormalMod
es/
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 http//www.calpoly.edu/gepstein/NormalMod
es/
8Interacting Pulses
9Interacting Pulses same direction