Calculator
Example Data Table
| Mode | Inputs | Frequency | Period |
|---|---|---|---|
| Spring-Mass | k = 200 N/m, m = 2 kg | 1.5915 Hz | 0.6283 s |
| Simple Pendulum | L = 1 m, g = 9.81 m/s² | 0.4985 Hz | 2.0061 s |
| LC Circuit | L = 10 mH, C = 100 µF | 159.1549 Hz | 0.0063 s |
| From Period | T = 0.25 s | 4 Hz | 0.25 s |
| Angular Frequency | ω = 31.4159 rad/s | 5 Hz | 0.2 s |
| Torsional | κ = 4 N·m/rad, I = 0.04 kg·m² | 1.5915 Hz | 0.6283 s |
Formula Used
Spring-Mass Oscillator: f = (1 / 2π) × √(k / m)
Use spring stiffness k and oscillating mass m. Greater stiffness raises frequency. Greater mass lowers frequency.
Simple Pendulum: f = (1 / 2π) × √(g / L)
This relation is based on the small-angle approximation. Shorter pendulums oscillate faster than longer ones.
LC Circuit: f = 1 / (2π√(LC))
Use inductance L and capacitance C. Larger L or C reduces the natural electrical oscillation frequency.
From Period: f = 1 / T
If one cycle takes T seconds, the system completes 1/T cycles each second.
From Angular Frequency: f = ω / (2π)
Angular frequency measures phase rate in radians per second. Divide by 2π to convert to cycles per second.
Torsional Oscillator: f = (1 / 2π) × √(κ / I)
Use torsional stiffness κ and moment of inertia I for rotational oscillation systems.
How to Use This Calculator
1. Select the model that matches your oscillating system.
2. Enter the known values and choose the correct units.
3. Click Calculate Frequency to place the result below the header and above the form.
4. Review the normalized inputs, computed outputs, and the plotted graph.
5. Use Download CSV for spreadsheet work or Download PDF for a printable report.
About Frequency of Oscillation
Frequency of oscillation tells you how many complete cycles a vibrating system finishes each second. It is a core measure in mechanics, electronics, acoustics, structural response, and signal analysis. A single calculator becomes more useful when it supports several physical models because real systems do not all behave the same way.
In a spring-mass system, stiffness and mass control the motion. Stronger springs pull the body back faster, while larger mass resists acceleration. In a pendulum, gravity and length matter. Short pendulums swing faster because the restoring effect acts over a smaller path. In an LC circuit, energy moves between magnetic and electric storage, creating electrical oscillation. Larger inductance or capacitance slows the exchange and lowers the frequency.
The period mode is practical when you already measured the time for one cycle. Angular frequency mode helps when vibration data or equations are written using radians per second. The torsional mode covers rotating bodies, shafts, and disks where angular stiffness and inertia define the response.
Using consistent units is important. A mismatch between grams and kilograms or microfarads and farads can shift the answer by a large factor. That is why this calculator normalizes the entered values before displaying the final results. It also returns extra outputs such as period, angular frequency, cycles per minute, revolutions per minute, and milliseconds per cycle. These related values help compare laboratory measurements, machine settings, and theoretical results.
The graph adds another layer of understanding. Instead of seeing only one answer, you can inspect how the frequency changes when a key parameter varies. This is helpful for design decisions, classroom examples, and quick checks during troubleshooting.
FAQs
1. What is frequency of oscillation?
It is the number of complete cycles finished each second. The standard unit is hertz, written as Hz.
2. What is the difference between frequency and period?
Frequency counts cycles per second. Period measures the time for one cycle. They are reciprocals, so f = 1/T and T = 1/f.
3. When should I use the pendulum formula?
Use it for a simple pendulum with small swing angles. Large amplitudes need more advanced treatment because the small-angle approximation becomes less accurate.
4. Why does mass reduce spring frequency?
A larger mass resists acceleration more strongly. That slows the oscillation, so the natural frequency becomes lower for the same spring stiffness.
5. Why does a larger capacitance lower LC frequency?
More capacitance stores more electric energy for the same voltage. That increases the oscillation time and decreases the circuit frequency.
6. Is angular frequency the same as regular frequency?
No. Angular frequency is in radians per second, while regular frequency is in cycles per second. They are related by ω = 2πf.
7. Can I export the results?
Yes. The page includes CSV export for data work and a PDF print option for saving a report through your browser.
8. What units does the calculator support?
It supports common units for mass, length, spring constant, inductance, capacitance, period, angular frequency, torsion constant, and moment of inertia.