Calculator inputs
Choose how the oscillation rate is defined, then evaluate the specified condition.
Example data table
This sample helps verify the calculator workflow.
| Parameter | Example value |
|---|---|
| Condition label | Reference check |
| Mode | Frequency based input |
| Amplitude A | 0.20 m |
| Mass m | 1.50 kg |
| Frequency f | 0.75 Hz |
| Initial phase φ₀ | 20 deg |
| Specified time t | 0.60 s |
| Equilibrium offset x₀ | 0.00 m |
| Computed ω | 4.712389 rad/s |
| Computed phase θ | 182.000000 deg |
| Displacement x-x₀ | -0.199878 m |
| Velocity v | 0.032892 m/s |
| Acceleration a | 4.438616 m/s² |
| Restoring force F | 6.657925 N |
| Total energy E | 0.666198 J |
Formula used
Meaning of symbols: A is amplitude, x₀ is equilibrium offset, φ₀ is initial phase, ω is angular frequency, f is frequency, T is period, k is spring constant, and m is mass.
Specified condition idea: The calculator evaluates the motion state at one chosen instant. That instant is the entered time t.
How to use this calculator
- Enter a label for the condition you want tested.
- Select how the oscillation rate is known.
- Enter amplitude, mass, initial phase, and specified time.
- Provide offset only if equilibrium is not zero.
- Submit the form to generate the result block.
- Review displacement, velocity, acceleration, force, and energy values.
- Inspect the Plotly graph for motion behavior over time.
- Export the results as CSV or PDF when needed.
Frequently asked questions
1) What does specified condition mean here?
It means the calculator evaluates motion at a chosen instant. Enter the time value, and it computes the phase, displacement, velocity, acceleration, force, and energies for that exact condition.
2) Can I use frequency, period, or spring constant?
Yes. The input mode lets you define the oscillation rate from angular frequency, ordinary frequency, period, or spring constant with mass. The page converts everything into angular frequency automatically.
3) Why is mass required?
Mass is needed for restoring force and energy calculations. Position and velocity depend on amplitude and frequency, but force and energies depend on the system mass too.
4) What is equilibrium offset?
Offset shifts the center position of the oscillation. If your motion oscillates around zero, keep it at zero. If the center is elsewhere, enter that value.
5) Does this page support negative phase angles?
Yes. Negative phase values are valid. They simply shift the starting point of the cosine wave backward relative to the chosen reference.
6) Why does velocity become zero sometimes?
Velocity becomes zero at turning points. Those points occur near maximum positive or negative displacement, where the oscillator reverses direction.
7) Why does acceleration point opposite displacement?
In simple harmonic motion, acceleration is restoring. It always acts toward equilibrium, so it has the opposite sign of the displacement from equilibrium.
8) What does the graph show?
The graph plots position, velocity, and acceleration over time. It helps you compare phase shifts, peaks, zero crossings, and the relation between different motion variables.
Notes
This calculator models ideal simple harmonic motion. It does not include damping, driving force, or nonlinear stiffness.