Analyze vibrations through wave, spring, pendulum, angular inputs. Get instant conversions, periods, wavelengths, and checks. Use clean exports, formulas, examples, and guidance for accuracy.
| Method | Inputs | Frequency | Note |
|---|---|---|---|
| Period | T = 0.02 s | 50 Hz | Fast oscillator with short cycle time. |
| Angular | ω = 314.159 rad/s | 50 Hz | Direct conversion from angular motion. |
| Wave | v = 340 m/s, λ = 0.68 m | 500 Hz | Typical sound wave style calculation. |
| Spring-Mass | k = 400 N/m, m = 0.25 kg | 6.3662 Hz | Natural frequency of a simple oscillator. |
| Pendulum | L = 1 m, g = 9.81 m/s² | 0.4985 Hz | Valid for small-angle oscillations. |
| String | L = 0.65 m, T = 120 N, μ = 0.008 kg/m, n = 1 | 94.2108 Hz | Fundamental frequency for a stretched string. |
The calculator supports several standard vibration relationships. Select the method matching your system, then enter values in any supported unit.
Period method
f = 1 / T
Angular frequency method
f = ω / (2π)
Wave method
f = v / λ
Spring-mass method
f = (1 / 2π) × √(k / m)
Simple pendulum method
f = (1 / 2π) × √(g / L)
Vibrating string method
fₙ = (n / 2L) × √(T / μ)
The result panel also shows period, angular frequency, cycles per minute, energy equivalent, and wavelength whenever enough information is available.
Vibrational frequency is the number of complete oscillations made in one second. It is usually measured in hertz, where one hertz equals one cycle per second.
Use the period method when you already know the time taken for one full cycle. It is the most direct way to convert measured timing into frequency.
It is most accurate for small-angle motion. Large swings change the motion enough that the simple small-angle frequency expression becomes less precise.
A stretched string can vibrate in multiple standing-wave patterns. The harmonic number selects which mode you want, changing both frequency and wavelength.
Angular frequency measures oscillation rate in radians per second. It links circular motion and vibration, and converts to ordinary frequency using division by 2π.
Wavelength requires both frequency and wave speed. If your selected method does not supply wave speed, enter the optional value to calculate wavelength.
The calculator also shows Planck-relation energy from E = hf. This is useful for comparing frequencies with quantum-style energy scales.
Yes. After calculating, use the CSV button for spreadsheet-style data or the PDF button for a clean report you can save or print.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.