Description
Energy change from a preloaded ideal linear spring, retaining the signed preload cross term.
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.
Energy change from a preloaded ideal linear spring, retaining the signed preload cross term.
When to use this tool
Use Spring Energy Preload Cross 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 stiffness, preload, displacement. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read crossTerm, incrementalEnergy. Use the output convention below.
For nonnegative stiffness return crossTerm=stiffness*preload*displacement and incrementalEnergy=crossTerm+stiffness*displacement^2/2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| stiffness | Spring stiffness in force per length units. | Required. Finite number; minimum 0. |
| preload | Signed initial spring extension in length units, not force. | Required. Finite number. |
| displacement | Signed displacement in the stated length unit, or vector components where declared. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| crossTerm | Cross Term | Required. Finite number. |
| incrementalEnergy | Incremental Energy | Required. Finite number. |
{
"input": {
"stiffness": 2,
"preload": 3,
"displacement": 4
},
"output": {
"crossTerm": 24,
"incrementalEnergy": 40
}
}Limitations and assumptions
- Preload means a signed initial spring extension, not a preload force. Use matching length units; incremental energy can be negative when motion releases stored energy, and nonlinear behavior is not modeled.
- 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
- Spring Series One Compliance Addend
For positive stiffness and nonnegative existingCompliance return compliance=existingCompliance+1/stiffness and equivalentStiffness=1/compliance.
- Spring Series Energy Share
Share stored energy between two ideal series springs carrying the same force.