Step Response Overshoot Calculator

Ideal underdamped second order unit-step overshoot,0<ζ<1; not measured nonlinear/system overshoot. Actual independently established compatible SI units/model context; conditional arithmetic, not code compliance, engineering design or safe operation approval.

Description

Ideal underdamped second-order step overshoot depends on damping ratio within a restricted branch.

Ideal underdamped second-order step overshoot depends on damping ratio within a restricted branch.^[1]

This tool calculates the model's percentage overshoot without measuring a nonlinear system response.

When to use Step Response Overshoot Calculator

Use this tool to calculate the model's percentage overshoot without measuring a nonlinear system response.

How to use Step Response Overshoot Calculator and how it works

Prepare dampingRatio, with the units, conventions and assumptions below.
Enter the required fields and run Step Response Overshoot Calculator.
Read result.value using the output definitions below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
dampingRatio	Dimensionless damping ratio zeta on the tool-specific branch below.	number	Required; strictly positive; finite; other constraints below

Supply damping ratio zeta strictly between zero and one. Return 100*exp(-pi*zeta/sqrt(1-zeta^2)) as percent overshoot for the canonical underdamped second-order step response. Critical and overdamped branches are rejected, and extra poles or zeros are not modeled.

overshootPercent=100*exp(-pi*zeta/sqrt(1-zeta^2))

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.value	Canonical second-order percent overshoot.	number

json

{
  "input": {
    "dampingRatio": 0.5
  },
  "output": {
    "result": {
      "value": 16.303353482158045
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Vibration Transmissibility Calculator for a complementary operation: An ideal single-degree-of-freedom transmissibility depends on damping and excitation-to-natural-frequency ratio.

Use Settling Time Calculator for a complementary operation: A specified exponential envelope reaches a chosen fraction according to its decay rate.

References

Step Response Overshoot Calculator — tool.io

Similar or alternative tools

Vibration Transmissibility Calculator
An ideal single-degree-of-freedom transmissibility depends on damping and excitation-to-natural-frequency ratio.
Settling Time Calculator
A specified exponential envelope reaches a chosen fraction according to its decay rate.