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Damped Simple Harmonic Motion

Equation

ω = ω_0 sqrt(1 - ζ^2) | | 
ω | angular frequency
ω_0 | natural angular frequency
ζ | damping ratio

Input values

natural angular frequency | 6 rad/s (radians per second)
damping ratio | 0.2

Result

angular frequency | 5.879 rad/s (radians per second)
= 336.8°/s (degrees per second)

Displacement vs. time


(assuming initially at rest)

Time derivative of displacement vs. time


(assuming initially at rest)

Angular frequency vs. damping ratio

Angular frequency vs. damping ratio

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