Vibration and Dynamics Simulators

Accelerometer Frequency Response Simulator

Modal Analysis

Accelerometer Frequency Response Simulator: An accelerometer is itself a tiny spring-mass-damper system. Adjust the natural frequency, damping ratio and the …

Base Excitation Transmissibility Simulator

SDOF & Damping

Base Excitation Transmissibility Simulator: Explore how well a spring-damper isolator blocks vibration arriving through the foundation. Adjust the system's n…

Base Isolation Period Shift Simulator

Seismic Dynamics

Estimate acceleration reduction, isolation displacement, and base shear from fixed-base period, isolated period, damping, building mass, and input PGA.

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

Campbell Diagram Simulator for rotor critical speeds: visualize whirl modes, gyroscopic effects, and engine-order intersections in real-time analysis.

Centrifugal Governor Simulator

Rotor Dynamics

Centrifugal Governor Simulator: Get a feel for the centrifugal governor (flyball governor) that James Watt made famous on his steam engine. Adjust the flybal…

Cepstrum Analysis Simulator — Speech & Vibration Analysis

Modal Analysis

Cepstrum Analysis Simulator for pitch detection and harmonic analysis. Learn real cepstrum computation, quefrency domain, vibration signal processing.

Chladni Figures Simulator — Vibration Modes of a Square Plate

Modal Analysis

Chladni Figures Simulator visualizes vibration modes and nodal lines on square plates using Ritz method. Explore eigenfrequencies and modal analysis for acoustic engineering and vibration research.

Coulomb Damping Simulator — Free Vibration with Dry Friction

SDOF & Damping

Coulomb Damping Simulator for free vibration analysis with dry friction. Model linear amplitude decay and finite stopping time in mass-spring systems.

Shaft Critical Speed Simulator

Rotor Dynamics

Shaft Critical Speed Simulator: Find the "critical speed" of a rotating shaft carrying a disc. Adjust the shaft diameter, span, disc mass and operating speed…

Damped Natural Frequency Simulator

Modal Analysis

Damped Natural Frequency Simulator: Explore the damped free vibration of a single-degree-of-freedom mass-spring-damper system when it is displaced and releas…

Double Pendulum Chaos Simulator — Lagrangian Dynamics & RK4 Integration

Pendulums & Nonlinear

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)

Seismic Dynamics

Visualize P-wave and S-wave propagation in solids with our free online simulator. Calculate velocities, see waveforms, and explore elastic wave fundamentals.

Liquid Sloshing Analysis — Natural Frequencies & Equivalent Pendulum

Seismic Dynamics

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

Pendulums & Nonlinear

Foucault pendulum simulator: latitude, length, g, and elapsed time give the swing period, precession rate, full-rotation time, and angle from Omega*sin(phi) with a top-down view.

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

SDOF & Damping

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…

Harmonic Motion Simulator (SHM, Damped, Driven)

SDOF & Damping

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

Pendulums & Nonlinear

Synthesize two orthogonal sinusoidal oscillations and observe beautiful Lissajous figure formation in real-time Canvas animation.

Lissajous Figures Simulator — Vibration & Wave Patterns

Pendulums & Nonlinear

Explore Lissajous figures: a simulator to create intricate patterns by tuning frequency, phase, and damping of two perpendicular oscillations.

Lissajous Figure & Vibration Synthesis Simulator

Pendulums & Nonlinear

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.

Magnetic Pendulum Chaos Simulator — Fractal Basin of Attraction

Pendulums & Nonlinear

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

Modal Analysis

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

Pendulums & Nonlinear

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.

Double Pendulum Chaos Simulator

Pendulums & Nonlinear

Double pendulum chaos simulator using 4th-order Runge-Kutta. Visualize two trajectories with initial angles offset by 0.001° to see the butterfly effect of chaos.

Double Pendulum Simulator — Chaotic Motion Visualization

Pendulums & Nonlinear

Simulate chaotic double pendulum motion in real time. Visualize how tiny initial changes create wildly different paths using Lagrangian mechanics and RK4 integration.

Large-Amplitude Pendulum Simulator — Period vs Amplitude

Pendulums & Nonlinear

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

Pendulums & Nonlinear

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

SDOF & 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

Response Spectrum Simulator for SDOF seismic design—adjust period, damping, PGA to compute design response, spectral acceleration, and site factors per IBC code.

Rotating Unbalance Vibration Simulator

Rotor Dynamics

Rotating Unbalance Vibration Simulator: Analyse the unbalance vibration of spring-supported rotating machinery such as motors, fans and pumps. Adjust the rot…

Rotor Balancing Simulator

Rotor Dynamics

When a fan, an impeller or a grinding wheel vibrates, the cause is almost always mass unbalance.

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

SDOF & Damping

Real-time frequency response function (FRF) calculator for single-degree-of-freedom systems. Interactively visualize resonance, damping ratio, and dynamic amplification factor.

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

Seismic design spectrum calculator for building natural period and soil type. Compute Sa(T), base shear force, and ground amplification effects.

Seismic Isolation Analysis Tool — Natural Period, Displacement & Response Spectrum

Seismic Dynamics

Analyze seismic isolation performance by adjusting building mass, stiffness, damping, and soil type. Instantly compute natural period, spectral acceleration, and displacements.

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

SDOF & Damping

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

Shock Response Spectrum Simulator: Numerically integrate the response of a single-degree-of-freedom (SDOF) system to a half-sine shock pulse. Adjust pulse am…

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

SDOF & Damping

Select Maxwell, Kelvin-Voigt, or SLS model to compute and visualize creep, stress relaxation, and dynamic viscoelasticity (E', E'', tanδ) in real time. With model schematic diagrams, intuitively understand viscoelastic material behavior.

Spring-Mass Oscillation Simulator

SDOF & Damping

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

Pendulums & Nonlinear

Spring Pendulum (Elastic Pendulum) Simulator: Watch spring stretching and pendulum swinging become coupled through nonlinear dynamics. RK4 integration reveal…'s nonlinear dynamics. Watch parametric resonance, energy transfer, and a colored trail showing 600-point motion history.

Spring-Mass-Damper System Analyzer (Static & Dynamic)

SDOF & Damping

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

Modal Analysis

Standing Wave Modes on a String: Visualize standing waves (fundamental and harmonics) on a string in real-time animation. Adjust tension, length, and linear …

Stick-Slip Friction Simulator — Self-Excited Vibration

Pendulums & Nonlinear

Stick-slip friction simulator for self-excited vibration analysis. Model periodic stick-slip cycles driven by static-kinetic friction differences. Interactive dry friction.

Elastic Stress Wave Propagation Simulator

Seismic Dynamics

Simulate stress wave propagation across material interfaces. Visualize reflection and transmission on a live Lagrange diagram. Compute wave speeds and acoustic impedance.

String Vibration Frequency Simulator

Modal Analysis

Free string vibration calculator: compute the fundamental and mode frequencies of a stretched string from length, tension and linear density using Mersenne's law. Wave speed, wavelength, period and nearest musical note are shown in real time.

Structural Dynamic Response Simulator (SDOF)

Modal Analysis

SDOF structural dynamic response simulator. Apply harmonic, impulse, random or El Centro motion and compute the response via RK4 in real time, with FRF 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

Solve torsional eigenvalue problems for 2- to 4-disc shaft systems. Computes natural frequencies, mode shapes and Campbell diagrams to find critical speeds.

Tuned Mass Damper Simulator

Modal Analysis

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

Modal Analysis

Simulate Tuned Mass Dampers (TMD) in real-time. Compare frequency response curves, observe anti-resonance, and apply Den Hartog's optimal tuning rules. Free online calculator.

Tuned Mass Damper (TMD) Simulator — Den Hartog Optimal Design

Modal Analysis

Adjust mass ratio μ, primary damping, and TMD parameters to see how vibration peaks are suppressed.

Vibration Signal Analyzer (Machinery Diagnostics)

SDOF & Damping

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

SDOF & Damping

Explore SDOF damped vibration responses in real-time. Adjust mass, stiffness, and damping to compare underdamped, critically damped, and overdamped systems.

Advanced Vibration Isolation Mount Design Calculator

SDOF & Damping

Calculate vibration transmissibility, isolation efficiency, and static deflection in real time. Design optimal mounts and visualize the resonance danger zone.

Vibration Isolation Mount Design Calculator

SDOF & Damping

Vibration isolator simulator for transmissibility analysis. Model displacement isolation using mass, stiffness, damping parameters across frequency ratios. CAE tool for engineers.

Vibration Measurement Analysis Tool — Acceleration/Velocity/Displacement & ISO 10816

Modal Analysis

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

SDOF & Damping

Calculate RMS stress, peak stress, and fatigue life using the Steinberg 3σ method for vibration analysis with PSD input. Free online calculator.