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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

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