mü + cu̇ + ku = F(t)
ω = √(k/m)
u(t) = Ae^(-ζωt)cos(ωdt + φ)
T = 2π/ω

CIE 512

Dynamics of Structures

Interactive Simulations & Visualizations
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Undamped Free Vibration

Explore the fundamental behavior of single-degree-of-freedom systems undergoing free vibration without damping.

Interactive mass-spring system • Real-time parameter adjustment • Time history analysis

Damped Free Vibration

Explore the effects of viscous damping on free vibration response with interactive comparisons.

Critical damping • Overdamped response • Underdamped oscillations • Envelope decay

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Harmonic Excitation

Analyze structural response to harmonic loading with real-time frequency response visualization.

Frequency response • Resonance • Dynamic amplification • Phase relationships

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Multi-DOF Systems

Coming Soon: Multi-degree-of-freedom system dynamics and modal analysis.

Natural modes • Modal superposition • Eigenvalue analysis