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Simple Harmonic Motion Position Calculator — result sheet
Evaluate displacement, velocity, and acceleration at a time in ideal sinusoidal motion from amplitude, frequency, and phase.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: ω = 2πf; x = A cos(ωt+φ); v = −Aω sin(ωt+φ); a = −Aω² cos(ωt+φ); vₘₐₓ = Aω.
Simple harmonic motion is the ideal sinusoidal solution for a restoring acceleration proportional to displacement. The phase input lets the same tool represent different points in the cycle.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Amplitude — length units; minimum 0; maximum 1000000000
- Frequency — Hz; minimum 1.0E-6; maximum 1000000000
- Time — s; minimum -1000000000; maximum 1000000000
- Phase — degrees; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Amplitude | 0.05 |
| Frequency | 2 |
| Time | 0.125 |
| Phase | 0 |
At 0.125 s: x = 0, v = −0.6283 length units/s, a = 0; maximum speed = 0.6283 length units/s.
Assumptions and limits
- The oscillator is undamped, sinusoidal, and described by the entered amplitude and frequency.
- Phase is entered in degrees and converted to radians.
- Driving forces, friction, nonlinear stiffness, and energy loss are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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