Lissajous Curve Parameters Calculator computes the frequency ratio and phase difference for a Lissajous curve. Input the x-frequency, y-frequency, and phase difference, select their units, and calculate the parameters.

How to Use Lissajous Curve Parameters Calculator:

1. Enter the x-frequency, y-frequency, and phase difference using the keypad or direct input; use “Next” to switch fields.
2. Select appropriate units for each parameter (e.g., Hz, kHz, MHz for frequencies; degrees, radians for phase difference).
3. Click “Calculate” to see step-by-step results.
4. Use “Share Result” to get shareable text or “Copy Result” to copy to clipboard.

Formulas:

Frequency Ratio (fₓ / fᵧ):

Phase Difference (δ): As input, in degrees or radians

Where: fₓ = x-frequency (Hz), fᵧ = y-frequency (Hz), δ = phase difference

Important Notes:

• Inputs for x-frequency and y-frequency must be positive numbers. Y-frequency cannot be zero (to avoid division by zero). Invalid inputs will trigger an error.
• The calculator assumes sinusoidal oscillations for the Lissajous curve.
• The frequency ratio determines the shape of the Lissajous curve, and the phase difference affects its orientation.
• Clipboard access requires a secure context (HTTPS). If copying fails, try accessing over HTTPS or copy manually.