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Focused engineering tools for fast, well-defined problems.
19 calculators · Dynamics & Control
Dynamics & Control
19 calculatorsDomain overview →
System Dynamics
- 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
- 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
- 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
- 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.