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Freebody Diagram
slopes
plot interpretation
Newton's 2nd Law
Graphical
...is a differential equation
Representation
Fourier Series
max acceleration
max velocity
Setting up Newton's 2nd Law
to get the differential equation
amplitude
complex behavior is the
superposition of many
similar simple behaviors
phase shift
http://coccweb.cocc.edu/bemerson/public_html/physics/PH213/213resources/HarmonicOscillatorProblems.doc
angular frequency =
http://www.falstad.com/fourier/
Falstad Fourier Exploration
frequency = f = 1/T
T = Period
repeated cycle
Periodic Motion
restoring force
linearization for small angles
Simple
quasi periodic
first derivative term
leads to damping
spatial or temporal
second order linear
Harmonic Motion
sine and cosine solutions
Differential Equations
MTH 256
requires linear differential equation
period driving term
damping constant
can be destructive
Damped Oscillations
driving frequency
natural frequency
exponential envelope
Driven Oscillations
significant engineering
forcing term
linear first order term