Calculator Form
Choose a resonance model, enter values, and generate results above this form. The layout uses three columns on large screens, two on medium screens, and one on mobile.
Example Data Table
| Model | Input Set | Sample Resonant Frequency | Comment |
|---|---|---|---|
| LC Circuit | L = 10 mH, C = 100 nF | 5032.921 Hz | Ideal LC resonance with matched reactance. |
| Series RLC | R = 15 Ω, L = 20 mH, C = 220 nF | 2397.866 Hz | Damping lowers resonance from the ideal LC case. |
| Parallel RLC | R = 1000 Ω, L = 50 mH, C = 470 nF | 981.436 Hz | Useful for tuned networks and filters. |
| Spring-Mass | k = 200 N/m, m = 0.5 kg | 3.183 Hz | Mechanical natural frequency of oscillation. |
| Open Pipe | v = 343 m/s, L = 0.75 m, n = 1 | 228.667 Hz | Fundamental frequency for an open tube. |
| Closed Pipe | v = 343 m/s, L = 0.85 m, n = 3 | 302.647 Hz | Only odd harmonics are valid here. |
Formula Used
Electrical Resonance
LC Circuit: f = 1 / (2π√LC)
Series RLC: f = (1 / 2π) √[(1 / LC) - (R² / 2L²)]
Parallel RLC: f = (1 / 2π) √[(1 / LC) - (1 / R²C²)]
Angular Frequency: ω = 2πf
Period: T = 1 / f
Series Q Factor: Q = (1 / R) √(L / C)
Parallel Q Factor: Q = R √(C / L)
Mechanical and Acoustic Resonance
Spring-Mass: f = (1 / 2π) √(k / m)
Open Pipe: f = nv / 2L
Closed Pipe: f = nv / 4L, where n is odd
Wavelength: λ = v / f
These equations assume idealized conditions. Real systems may shift because of losses, damping, temperature, geometry, or parasitic effects.
How to Use This Calculator
- Select the resonance model that matches your physical system.
- Enter each value with the correct unit from the dropdowns.
- Use an odd harmonic for closed pipes, such as 1, 3, or 5.
- Press Calculate Resonance to display results above the form.
- Review the frequency, angular frequency, period, and any extra metrics.
- Inspect the Plotly graph to see how the chosen variable changes resonance.
- Use the CSV button for spreadsheet work and the PDF button for reports.
- Compare your values with the example table to validate input reasonableness.
FAQs
1. What does resonant frequency mean?
Resonant frequency is the natural frequency where a system responds most strongly. At that point, energy transfer becomes efficient, and oscillation amplitude can rise sharply when damping is small.
2. Why are there several resonance models here?
Resonance appears in circuits, springs, and air columns. Each system follows different physics, so the calculator includes electrical, mechanical, and acoustic formulas in one page.
3. What is the difference between LC and RLC resonance?
An ideal LC circuit ignores resistance. RLC resonance includes resistance, so damping changes the resonant point, lowers the sharpness of the peak, and affects bandwidth.
4. Why does the closed-pipe model require odd harmonics?
A closed pipe has a node at one end and an antinode at the other. That boundary condition only supports odd harmonic modes, such as 1, 3, 5, and 7.
5. How does damping affect resonance?
Damping reduces peak response and can slightly shift the observed resonant frequency. In RLC systems, resistance is the damping source. In mechanical systems, friction and material losses contribute.
6. What does the Q factor tell me?
Q factor measures how selective or sharp the resonance is. Higher Q means lower energy loss, narrower bandwidth, and a more pronounced resonance peak near the natural frequency.
7. Can I use this calculator for real lab measurements?
Yes, it is useful for estimation, planning, and checking measurements. Real systems may differ because of tolerance, parasitic elements, temperature, damping, and non-ideal boundary conditions.
8. Why does the graph change one variable only?
The graph is designed to show sensitivity clearly. By sweeping one major input while holding others fixed, you can quickly see how resonance shifts and compare design tradeoffs.