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Dynamics Of Rigid Bodies2D

Mechanical Vibrations - Theory & Concepts

Introduction to free and forced vibrations of single-degree-of-freedom systems, including torsional vibrations and damping.

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Mechanical Vibrations — Mass-Spring-Damper SystemUnderdamped (ζ = 0.06)

System Parameters

Vibration Equations

Equation of Motion:
mx¨+cx˙+kx=0m\ddot{x} + c\dot{x} + kx = 0
ωn=km=3.16 rad/s\omega_n = \sqrt{\frac{k}{m}} = 3.16\,\text{rad/s}
ζ=ccc=c2km=0.063\zeta = \frac{c}{c_c} = \frac{c}{2\sqrt{km}} = 0.063
ωd=ωn1−ζ2=3.16 rad/s\omega_d = \omega_n\sqrt{1-\zeta^2} = 3.16\,\text{rad/s}
x(t):1.0000 m
ẋ(t):-0.0250 m/s
ẍ(t):-4.993 m/s²
t:0.00 s
Mechanical Vibration Model and Responsekceq.m+1.00mt(s)x(m)036912-1.00.01.0UnderdampedModelResponse x(t)

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