Description
For dampingRatio in [0,1) return logDecrement=2*pi*zeta/sqrt(1-zeta^2) and amplitudeRatio=exp(-logDecrement).
A mechanics calculation needs a coordinate frame, sign convention, and consistent force, length, mass, and time units. Vector projections, local balance terms, and ideal motion equations describe particular parts of a physical model. They do not automatically establish all equilibrium conditions or the validity of the model.
For dampingRatio in [0,1) return logDecrement=2*pi*zeta/sqrt(1-zeta^2) and amplitudeRatio=exp(-logDecrement).
When to use this tool
Use Viscous Damping Log Decrement Pair when you need this particular projection, balance, frame conversion, or ideal-model component from supplied physical quantities.
How to use the tool and how it works
- Enter dampingRatio. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read logDecrement, amplitudeRatio. Use the output convention below.
For dampingRatio in [0,1) return logDecrement=2*pi*zeta/sqrt(1-zeta^2) and amplitudeRatio=exp(-logDecrement).1
An underdamped linear oscillator has an exponentially decaying amplitude. Critical and overdamped responses do not provide the successive oscillatory peaks assumed by this decrement calculation.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| dampingRatio | Dimensionless damping ratio zeta in [0,1). | Required. Finite number; minimum 0; strictly below 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| logDecrement | Log Decrement | Required. Finite number. |
| amplitudeRatio | Next same-sign peak amplitude divided by the preceding amplitude. | Required. Finite number. |
{
"input": {
"dampingRatio": 0
},
"output": {
"logDecrement": 0,
"amplitudeRatio": 1
}
}Limitations and assumptions
- This is the ratio of successive same-sign peaks for an ideal underdamped linear oscillator. Zero damping returns one; critical and overdamped motion are excluded, and measurement fitting is separate.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete force, motion, or energy model when a single contribution is insufficient. Check coordinate frames, idealizations, and dimensional consistency before combining calculated terms.
References
-
Calculation and input contract: physics/viscous-damping-log-decrement-pair — tool.io
-
University Physics Volume 1: Damped Oscillations — OpenStax, Rice University
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