Description
For positive mass and nonnegative angularFrequency return kinetic=mass*velocity^2/2, potential=mass*(angularFrequency*position)^2/2, and energy=kinetic+potential.
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 positive mass and nonnegative angularFrequency return kinetic=mass*velocity^2/2, potential=mass*(angularFrequency*position)^2/2, and energy=kinetic+potential.
When to use this tool
Use Harmonic Oscillator Phase Space Energy 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 mass, angularFrequency, position, velocity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read kinetic, potential, energy. Use the output convention below.
For positive mass and nonnegative angularFrequency return kinetic=mass*velocity^2/2, potential=mass*(angularFrequency*position)^2/2, and energy=kinetic+potential.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| mass | Mass in a consistent unit for the stated model. | Required. Finite number; strictly above 0. |
| angularFrequency | Angular frequency in radians per chosen time unit. | Required. Finite number; minimum 0. |
| position | Position | Required. Finite number. |
| velocity | Velocity | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| kinetic | Kinetic | Required. Finite number. |
| potential | Potential | Required. Finite number. |
| energy | Energy | Required. Finite number. |
{
"input": {
"mass": 2,
"angularFrequency": 3,
"position": 2,
"velocity": 4
},
"output": {
"kinetic": 16,
"potential": 36,
"energy": 52
}
}Limitations and assumptions
- Position is displacement from equilibrium and angular frequency uses radians per time unit. The ideal harmonic model omits damping, drive, nonlinear stiffness, and any verification of oscillator parameters.
- 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
- Elastic Energy Strain One Mode
Return one linear elastic uniaxial mode energy, excluding plasticity and multiaxial coupling.
- Gravitational Potential Datum Energy Term
For nonnegative mass return energyShift=mass*potentialShift.