Domain
Dynamics & Control
Dynamics & Control on Anemodia: first- and second-order systems, transfer functions, stability, root locus, PID and classical control design, vibrations, modal analysis and state space.
Every tool below is solved by the same typed Dynamics & Control computation modules, so a calculator and the Lab it hands off to can never disagree. Calculators answer one well-posed question; Labs keep a whole model on screen — inputs, responses, diagrams and derived quantities together.
System Dynamics
First- and second-order response: time constants, natural frequency, damping ratio, overshoot and settling time.
First-Order Systems
availableAnalyze first-order dynamics, standard inputs, time constants and response metrics.
Dynamics & Control
Open Lab →
Second-Order Systems
availableAnalyze, compare and design canonical second-order systems.
Dynamics & Control
Open Lab →
- First-Order System CalculatorPole, DC gain, time constant, 10–90% rise time and settling estimates of the standard lag G(s) = K/(τs + 1).
- Damping Ratio CalculatorDamping ratio ζ implied by a percent overshoot of the canonical second-order step response.
- Percent Overshoot CalculatorPercent overshoot of the unit-step response for a given damping ratio ζ, with the damping regime.
- Settling Time CalculatorApproximate 2% and 5% settling times from ζ and ωn, within the underdamped envelope approximation.
- Damped Natural Frequency CalculatorDamped natural frequency ωd from undamped natural frequency ωn and damping ratio ζ.
- Second-Order System CalculatorAll canonical second-order response characteristics for a given ωn and ζ: regime, poles, ωd, overshoot, peak time and settling estimates.
Transfer Functions & Stability
General continuous-time LTI transfer functions, poles and zeros, frequency response, stability criteria and root locus.
Transfer Function Analysis
availableAnalyze general continuous-time LTI transfer functions in time, frequency and stability domains.
Dynamics & Control
Open Lab →
Root Locus
availableTrace closed-loop pole motion against a scalar gain, with stability ranges and the response at the selected gain.
Dynamics & Control
Open Lab →
- Transfer Function CalculatorOrder, relative degree, properness, DC gain, poles, zeros and stability of a transfer function entered as numerator and denominator coefficients.
- Poles and Zeros CalculatorPoles and zeros with multiplicities, half-plane classification, right-half-plane zero count and an s-plane map.
- Bode Plot CalculatorExact magnitude and phase against frequency, with break frequencies, asymptotic slopes, resonance and bandwidth where they are defined.
- Routh–Hurwitz Stability CalculatorRouth array, first-column sign changes, right-half-plane root count and Hurwitz determinants for a real characteristic polynomial.
Control
P, PI, PD, PID and lead/lag design, steady-state error and stability margins.
- Gain and Phase Margin CalculatorEvery gain and phase crossover of a loop transfer function, with finite, infinite or undefined margin semantics and multiple-crossing warnings.
- Steady-State Error CalculatorSystem type, Kp, Kv, Ka and the steady-state error of a unity-feedback loop to step, ramp and parabolic references.
- Root Locus CalculatorRoot locus of 1 + K·G(s) = 0: branches, asymptotes, breakaway points, imaginary-axis crossings, stable gain range and the closed-loop poles at a chosen gain.
- PID Controller CalculatorClosed-loop poles, stability verdict, overshoot, settling time, steady-state step error and margins of a unity-feedback loop with C(s) = Kp + Ki/s + Kd·s.
Vibrations & Modal
Single-degree-of-freedom vibration, resonance, transmissibility and isolation, plus multi-degree-of-freedom natural frequencies, mode shapes and FRFs.
Vibrations (Mass–Spring–Damper)
availableFree, forced, harmonic and base-excited single-degree-of-freedom vibration: resonance, transmissibility, isolation and energy.
Dynamics & Control · Engineering Mechanics
Open Lab →
Modal Analysis (2DOF & MDOF)
availableNatural frequencies, mode shapes, orthogonality, Rayleigh and modal damping, modal superposition, participation factors and receptance FRFs for M q̈ + C q̇ + K q = f(t).
Dynamics & Control · Engineering Mechanics
Open Lab →
- Mass–Spring–Damper CalculatorNatural frequency, critical damping, ζ, regime, damped frequency and period, logarithmic decrement, Q, poles and X/F for an SDOF system.
- Natural Frequency CalculatorUndamped natural frequency, natural period, critical damping and damping ratio of a mass–spring–damper system from m, c and k.
- Vibration Isolation CalculatorAbsolute displacement transmissibility, force transmissibility and relative displacement ratio of an SDOF mount at a given excitation frequency.
- 2DOF Natural Frequencies CalculatorUndamped natural frequencies and mass-normalized mode shapes of a two-degree-of-freedom mass–spring chain, from K φ = ω² M φ.
State Space
State-space realisations, eigenvalues, controllability and observability, and full-state-feedback pole placement.