Coupled Oscillator Frequencies Calculator
Coupled Oscillator Frequencies Calculator computes the normal mode frequencies for two identical masses coupled by springs. Input the mass, outer spring constant, coupling spring constant, select units, and calculate the frequencies.
Enter Parameters
How to Use Coupled Oscillator Frequencies Calculator:
- Enter the mass of each oscillator (m), outer spring constant (k), and coupling spring constant (k_c) using the keypad or direct input; use “Next” to switch fields.
- Select appropriate units for mass (kg, g) and spring constants (N/m, mN/m).
- Click “Calculate” to see step-by-step results for the normal mode frequencies.
- Use “Share Result” to get shareable text or “Copy Result” to copy to clipboard.
Formulas:
Normal Mode Frequencies:
ω₁ = √(k/m)
ω₂ = √((k + 2k_c)/m)
ω₂ = √((k + 2k_c)/m)
Where: ω₁ = symmetric mode frequency (rad/s), ω₂ = antisymmetric mode frequency (rad/s), m = mass of each oscillator (kg), k = outer spring constant (N/m), k_c = coupling spring constant (N/m)
Important Notes:
- Inputs for mass and spring constants must be positive. Invalid inputs will trigger an error.
- The calculator assumes two identical masses connected by three springs (two outer springs with constant k, one coupling spring with constant k_c).
- Clipboard access requires a secure context (HTTPS). If copying fails, try accessing over HTTPS or copy manually.