Description
Return only the leading amplitude-squared correction to the small-angle simple-pendulum period.
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.
Return only the leading amplitude-squared correction to the small-angle simple-pendulum period.
When to use this tool
Use Pendulum Small Angle Error Term 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 amplitudeRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read relativePeriodCorrection. Use the output convention below.
Return relativePeriodCorrection=amplitudeRadians^2/16.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| amplitudeRadians | Angular amplitude in radians; no small-angle validity bound is enforced. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| relativePeriodCorrection | Relative Period Correction | Required. Finite number. |
{
"input": {
"amplitudeRadians": 0.4
},
"output": {
"relativePeriodCorrection": 0.010000000000000002
}
}Limitations and assumptions
- This is the leading small-amplitude correction to an ideal pendulum's period ratio, not an exact period. The input is radians and the code does not enforce the small-angle regime or bound approximation error.
- 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
Similar or alternative tools
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