Simulator Library
Vibration and Dynamics Simulators
Vibration simulators for SDOF/MDOF response, modal analysis, damping, isolation, rotors, and seismic dynamics.
69 simulators
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Simulator list
Accelerometer Frequency Response Simulator
Modal Analysis
An accelerometer is itself a tiny spring-mass-damper system.
Base Excitation Transmissibility Simulator
Explore how well a spring-damper isolator blocks vibration arriving through the foundation.
Base Isolation Period Shift Simulator
Seismic Dynamics
Compare response spectrum, isolator displacement, and base-shear reduction to see how period shift and damping work together.
Beam Vibration Modes — Natural Frequencies & Mode Shapes
Modal Analysis
Visualize and animate natural vibration modes for beams. Superimpose modes to see combined effects and explore natural frequencies.
Campbell Diagram Simulator — Rotor Critical Speeds
Rotor Dynamics
Visualize two-mode natural frequencies, gyroscopic forward/backward whirl branches, and engine-order lines (1x, 2x, 3x). All critical speeds and the margin to the operat…
Centrifugal Governor Simulator
Get a feel for the centrifugal governor (flyball governor) that James Watt made famous on his steam engine. Adjust the flyball mass, central sleeve load, arm length and …
Cepstrum Analysis Simulator — Speech & Vibration Analysis
Compute the real cepstrum by inverse Fourier transform of the log magnitude spectrum. Change fundamental frequency, sample rate, and harmonic decay to learn pitch detect…
Chladni Figures Simulator — Vibration Modes of a Square Plate
Modal Analysis
Builds the vibration mode φ_mn(x,y) on a square plate by Ritz combination and renders Chladni nodal lines with the relative eigenfrequency. Sweep mode (m,n), mix α, and …
Coulomb Damping Simulator — Free Vibration with Dry Friction
Visualize the free vibration of a mass-spring system with dry friction. Unlike viscous damping, the amplitude decays linearly, the motion stops in finite time, and the r…
Shaft Critical Speed Simulator
Rotor Dynamics
Find the "critical speed" of a rotating shaft carrying a disc.
Damped Natural Frequency Simulator
Modal Analysis
Explore the damped free vibration of a single-degree-of-freedom mass-spring-damper system when it is displaced and released.
Double Pendulum Chaos Simulator — Lagrangian Dynamics & RK4 Integration
Simulate chaotic double pendulum physics in real time. Adjust lengths, masses, and angles to explore Lagrangian mechanics and RK4 integration.
Drumhead Vibration Simulator — Bessel Modes of a Circular Membrane
Modal Analysis
Drumhead vibration simulator. Vary radius R, tension T, surface density ρ_s, and mode index to compute eigenfrequencies f_mn from the Bessel-zero α_mn in real time.
Eigenvalue Analysis
Modal Analysis
Interactive simulator for multi-DOF spring-mass systems. Calculate natural frequencies, visualize mode shapes with animation, and explore real-time frequency response.
Elastic Wave Propagation Simulator (P-wave & S-wave)
Visualize P-wave and S-wave propagation in solids with our . Calculate velocities, see waveforms, and explore elastic wave fundamentals.
Liquid Sloshing Analysis — Natural Frequencies & Equivalent Pendulum
Calculate sloshing natural frequencies in rectangular tanks. Adjust dimensions, fluid depth & density to analyze 5 modes with key formulas.
Foucault Pendulum Simulator — Earth Rotation Precession
Adjust latitude, pendulum length, gravity, and elapsed time and watch the swing plane of a Foucault pendulum slowly rotate under Earth rotation. Omega*sin(phi) gives the…
Natural Frequency & Vibration Mode Calculator — Beams & Strings
Modal Analysis
Calculate beam or string natural frequencies and vibration modes. Select boundary conditions, enter properties, and view animated results instantly.
Frequency Response Function (FRF) Calculator — Bode Plot, Resonance, Damping
Modal Analysis
Calculate Frequency Response Function (FRF) Bode plots in real-time. Input natural frequency & damping ratio to get resonance, Q factor, and half-power bandwidth.
Half-Power Bandwidth Damping Simulator
Explore the half-power bandwidth (3 dB) method, which measures the damping ratio ζ from the width of a resonance peak in the frequency response function of a single-degr…
Harmonic Motion Simulator (SHM, Damped, Driven)
Compare simple harmonic, damped, and driven oscillations. Visualize resonance, Q-factor, and amplitude with interactive simulations and key physics equations.
Lamb Wave Dispersion Simulator — Plate S_0/A_0 Modes
Modal Analysis
Lamb wave dispersion simulator: real-time S_0 and A_0 phase velocity and wavelength for thin plates, with adjustable Young's modulus, density, frequency and thickness.
Lissajous Curves Simulator
Synthesize two orthogonal sinusoidal oscillations and observe beautiful Lissajous figure formation in real-time Canvas animation. Includes oscilloscope waveform view, ph…
Lissajous Figures Simulator — Vibration & Wave Patterns
Explore Lissajous figures: a simulator to create intricate patterns by tuning frequency, phase, and damping of two perpendicular oscillations.
Lissajous Figure & Vibration Synthesis Simulator
Synthesize two sine waves to create Lissajous figures. Adjust frequency, amplitude, and phase in real time and explore open or closed periodic curves.
Logarithmic Decrement Damping Simulator
Modal Analysis
Strike an object once, let it ring freely, and measure how its motion dies away. Enter the first peak amplitude and the peak n cycles later to see the logarithmic decrem…
Magnetic Pendulum Chaos Simulator — Fractal Basin of Attraction
Explore chaotic motion with a magnetic pendulum simulator. Visualize fractal basins of attraction by color-coding each point's final magnet.
3-DOF Mass-Spring System & Dynamic Vibration Absorber Simulator
Explore a 3-DOF mass-spring system. Adjust parameters, analyze vibrations, and add a Dynamic Vibration Absorber (DVA) to see its effect.
1D FEM Modal Analysis Simulator — Natural Frequencies & Mode Shapes
Modal Analysis
Simulate 1D rod vibration modes. Assemble stiffness & mass matrices, solve eigenvalue problems, and animate mode shapes with this FEM modal analysis tool.
Modal Analysis Simulator — 2-DOF Spring-Mass System
Modal Analysis
Explore natural frequencies, mode shapes, and FRF in real time. Adjust mass and stiffness in a 2-DOF spring-mass simulator with live animations.
Nonlinear Vibration Calculator
Visualize Duffing oscillator dynamics: frequency response curves, hardening/softening springs, jump phenomenon, and backbone curve via harmonic balance method.
Parametric Oscillator Simulator — Mathieu Equation, Stability Diagram
Modal Analysis
Simulate parametric resonance with the Mathieu equation. Adjust modulation to explore stability diagrams, time-domain responses, and phase portraits.
Large-Amplitude Pendulum Simulator — Period vs Amplitude
Large-amplitude pendulum simulator: real-time small-angle period T0=2pi*sqrt(L/g) and exact period via elliptic integral K(k), with period error and potential energy.
Pendulum Wave Simulator
Watch 15 pendulums create mesmerizing waves, spirals, and chaos through precise physics. A stunning visual demonstration of harmonic motion.
Rayleigh-Ritz Method Natural Frequency Estimator
Modal Analysis
Visualize the Rayleigh-Ritz method: adjust an assumed mode shape and see the frequency converge. Understand the upper-bound theorem for natural vibration analysis.
Resonance Frequency Simulator — Forced Vibration, Q Factor & Damping
Explore resonance with a real-time simulator. Adjust mass, stiffness, and damping to visualize curves and calculate Q factor, bandwidth, and phase lag.
Response Spectrum Simulator — SDOF Seismic Design Response
Seismic Dynamics
Real-time IBC design response spectrum. Vary period $T$, damping $\\zeta$, PGA and site factor to read $S_{DS}$, $S_{D1}$, transition period $T_S$ and current $S_a$.
Rotating Unbalance Vibration Simulator
Rotor Dynamics
Analyse the unbalance vibration of spring-supported rotating machinery such as motors, fans and pumps.
Rotor Balancing Simulator
Rotor Dynamics
When a fan, an impeller or a grinding wheel vibrates, the cause is almost always mass unbalance. Enter the original vibration, the vibration with a trial weight, and the…
Rotor Dynamics Critical Speed Calculator
Rotor Dynamics
Calculate rotor critical speed and unbalance response. Input mass, stiffness, eccentricity, and damping. Visualize the response curve and see animations.
Random Vibration Analysis Tool (PSD Input)
Seismic Dynamics
Analyze SDOF random vibration response in real time. Compute response spectrum, RMS, and 3-sigma values from your input PSD with adjustable 3-segment profiles.
SDOF Frequency Response Analysis Tool
Vary damping ratio and natural frequency to visualize the Frequency Response Function (FRF) in real time. Intuitively understand resonance mechanism and dynamic magnific…
Seismic Design Simulator — Response Spectrum & Story Shear
Seismic Dynamics
Real-time seismic design simulator: compute base shear, period, and story drift. Adjust building stories and site class for instant analysis.
Seismic Hazard Response Spectrum Calculator — Sa(T) & Base Shear
Seismic Dynamics
Set building natural period, soil type, and regional seismic coefficient to calculate design response spectrum Sa(T) and base shear force V in real time. Visualize groun…
Seismic Isolation Analysis Tool — Natural Period, Displacement & Response Spectrum
Seismic Dynamics
Adjust building mass, isolator stiffness, damping ratio and soil type to instantly compute natural period, peak Sa, isolator displacement and acceleration reduction vs f…
Seismic Response Spectrum (Sa/Sv/Sd) Simulator
Seismic Dynamics
The response spectrum is the core tool of earthquake-resistant design: for a structure with period T and damping zeta, it gives the maximum acceleration Sa(T), pseudo-ve…
Seismic Response Spectrum Calculator
Seismic Dynamics
Interactively compute design response spectra (Japan Building Code / ASCE/SEI 7 simplified model) and SDOF seismic response. Visualize Sa, Sv, Sd spectra in real time.
Shock Absorber / Vehicle Suspension Analysis
Simulate vehicle suspension dynamics with the quarter-car model. Analyze ride comfort per ISO 2631 standards and vibration transmissibility for optimal handling.
Shock Response Spectrum Simulator
Seismic Dynamics
Numerically integrate the response of a single-degree-of-freedom (SDOF) system to a half-sine shock pulse.
Spring Constant Calculator — Coil Spring, Leaf Spring & Natural Frequency
Modal Analysis
Calculate spring constant, solid length, index, and frequency for helical and leaf springs with our free real-time calculator.
Spring-Dashpot Viscoelastic Model Simulator — Maxwell & Kelvin-Voigt
Select Maxwell, Kelvin-Voigt, or Standard Linear Solid (SLS) model to calculate creep, stress relaxation, and dynamic viscoelasticity (E', E'', tan δ) in real time. Incl…
Spring-Mass Oscillation Simulator
Explore a 1DOF spring-mass-damper simulator. Adjust parameters in real-time to visualize overdamped, critically damped, and underdamped vibrations.
Spring Pendulum (Elastic Pendulum) Simulator — Parametric Resonance & Chaos
Simulate a spring pendulum's nonlinear dynamics. Watch parametric resonance, energy transfer, and a colored trail showing 600-point motion history.
Spring-Mass-Damper System Analyzer (Static & Dynamic)
Analyze series, parallel & mixed spring-mass-damper systems. Calculate static deflection, natural frequency, damping ratio, and dynamic step response.
Standing Wave Modes on a String
Visualize standing waves (fundamental and harmonics) on a string in real-time animation. Adjust tension, length, and linear density to experience changes in natural freq…
Stick-Slip Friction Simulator — Self-Excited Vibration
Visualize the self-excited stick-slip vibration of a mass pulled through a spring on a dry friction surface. The gap between static and kinetic friction drives a periodi…
String Vibration Frequency Simulator
Modal Analysis
Find the pitch of a plucked, struck or bowed string from its length, tension and linear density. The simulator shows the fundamental frequency, mode shape, wavelength, p…
Structural Dynamic Response Simulator (SDOF)
Simulate structural dynamics with an SDOF system. Apply harmonic, impulse, random, or El Centro ground motion and compute response via RK4. View real-time plots.
Torsional Pendulum Simulator — Natural Frequency & Period Calculator
Modal Analysis
Simulate torsional pendulums. Adjust shaft & disk parameters to instantly compute natural frequency, stiffness, and period. Visualize oscillations.
Torsional Vibration Analysis — Multi-DOF Shaft System
Rotor Dynamics
Compute natural frequencies, mode shapes & Campbell diagrams for 2–4 disc torsional shaft systems. Identify critical speeds for engines and turbines in real time.
Tuned Mass Damper Simulator
Design the tuned mass damper (TMD) that tames the sway of a tall building or a long-span bridge using Den Hartog optimal-TMD theory.
2-DOF Coupled Vibration & Dynamic Absorber Simulator
Simulate Tuned Mass Dampers (TMD) in real-time. Compare frequency response curves, observe anti-resonance, and apply Den Hartog's optimal tuning rules. .
Tuned Mass Damper (TMD) Simulator — Den Hartog Optimal Design
Optimize TMD design with Den Hartog's method. Adjust mass ratio and damping to suppress vibration peaks in this interactive simulator.
Vibration Signal Analyzer (Machinery Diagnostics)
Simulate bearing defects, imbalance & misalignment. Learn machine health monitoring principles with FFT and envelope analysis for predictive maintenance.
Vibration Damping Simulator — SDOF Damped Response & Logarithmic Decrement
Explore SDOF damped vibration responses in real-time. Adjust mass, stiffness, and damping to compare underdamped, critically damped, and overdamped systems.
Vibration Isolation Mount Design Calculator
Real-time displacement transmissibility from base to equipment. Vary mass, stiffness, damping, and forcing frequency to watch the TR-r curve cross the r=√2 boundary into…
Vibration Isolator Simulator — Transmissibility TR & Frequency Ratio
Real-time displacement transmissibility from base to equipment. Vary mass, stiffness, damping, and forcing frequency to watch the TR-r curve cross the r=√2 boundary into…
Vibration Measurement Analysis Tool — Acceleration/Velocity/Displacement & ISO 10816
Convert vibration data between acceleration, velocity & displacement. Get ISO 10816 health ratings and visualize A-weighted spectra instantly.
Vibration Fatigue PSD Stress Calculator — Steinberg 3σ Method
Calculate RMS stress, peak stress, and fatigue life using the Steinberg 3σ method for vibration analysis with PSD input. .
How to Use
- Select system type (SDOF, MDOF, or modal) and define material properties: mass (kg), stiffness (N/m), damping ratio (0–0.3 for typical structures)
- Input excitation parameters: frequency (Hz), amplitude (m/s²), or seismic acceleration time-history data
- Run simulation to generate frequency response functions (FRF), time-domain displacement/acceleration plots, and natural frequencies in rad/s
Worked Example
Steel frame with mass 5000 kg, stiffness 2.5×10⁶ N/m, damping ratio 0.08. Natural frequency ωn = √(k/m) = 22.4 rad/s (3.57 Hz). Under 0.5g seismic acceleration (ASCE 7-16), peak displacement reaches 18.3 mm and base shear = 2450 kN. Modal analysis reveals second mode at 58 rad/s contributes 12% to total response.
Practical Notes
- Use logarithmic scaling for FRF plots when examining resonance peaks across wide frequency ranges (0.1–100 Hz industrial machinery)
- Damping values: 0.02–0.05 for steel structures, 0.05–0.10 for reinforced concrete, 0.15–0.30 for elastomeric isolators
- Validate MDOF results against modal participation factors; modes with <2% mass participation typically negligible