Calculate resonant frequency for LC circuits (f = 1/(2π√(LC))) or mechanical systems (f = (1/(2π))√(k/m)). Free online physics calculator for electronics and mechanics with step-by-step solutions.
Calculate resonant frequency for LC circuits or mechanical systems
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Resonant frequency is a fundamental concept in physics and engineering that describes the natural frequency at which a system oscillates with maximum amplitude when subjected to a periodic driving force. Whether you're designing electronic circuits, analyzing mechanical systems, or studying wave phenomena, understanding resonant frequency is essential. Our Resonant Frequency Calculator makes it easy to calculate resonant frequency for two common scenarios: LC circuits (f = 1/(2π√(LC))) and mechanical spring-mass systems (f = (1/(2π))√(k/m)).
At resonance, a system responds with maximum amplitude to an external driving force. This phenomenon occurs in electrical circuits, mechanical systems, acoustic systems, and many other physical systems. Understanding and controlling resonant frequency is crucial for designing filters, oscillators, antennas, and vibration control systems.
Our Resonant Frequency Calculator supports two calculation modes:
Simply select your calculation mode, enter the required values, choose your units, and click Calculate to get instant results with step-by-step solutions.
Resonant frequency is calculated differently depending on the system type:
f = 1/(2π√(LC))
Where: f = resonant frequency, L = inductance, C = capacitance
This formula calculates the resonant frequency of an LC (inductor-capacitor) circuit. At this frequency, the circuit exhibits maximum impedance (for parallel LC) or minimum impedance (for series LC). LC circuits are fundamental components in radio frequency (RF) circuits, filters, and oscillators.
f = (1/(2π))√(k/m)
Where: f = natural/resonant frequency, k = spring constant, m = mass
This formula calculates the natural frequency of a simple harmonic oscillator (spring-mass system). At this frequency, the system oscillates with maximum amplitude when driven by an external force. This principle applies to mechanical vibrations, structural dynamics, and many engineering applications.
Resonant frequency calculations are used in countless real-world scenarios:
Resonant frequency calculations use various units depending on the application:
Common Values:
Calculate the resonant frequency of an LC circuit with L = 10 μH and C = 100 pF.
L = 10 μH = 10 × 10⁻⁶ H = 0.00001 H
C = 100 pF = 100 × 10⁻¹² F = 0.0000000001 F
f = 1/(2π√(LC)) = 1/(2π√(0.00001 × 0.0000000001))
f = 1/(2π × 0.000001) = 159,155 Hz ≈ 159.2 kHz
A spring-mass system has a spring constant of 500 N/m and a mass of 2 kg. What is its natural frequency?
k = 500 N/m, m = 2 kg
f = (1/(2π))√(k/m) = (1/(2π))√(500/2)
f = (1/(2π))√250 = (1/(2π)) × 15.81 = 2.52 Hz
An RF circuit uses L = 0.5 μH and C = 10 pF. Calculate the resonant frequency.
L = 0.5 μH = 0.5 × 10⁻⁶ H
C = 10 pF = 10 × 10⁻¹² F
f = 1/(2π√(0.5 × 10⁻⁶ × 10 × 10⁻¹²))
f = 1/(2π × 7.071 × 10⁻⁹) = 22.5 MHz
Understanding the difference between resonant frequency and other frequency concepts is important:
When the driving frequency matches the resonant frequency, the system exhibits resonance, which can be beneficial (tuning circuits) or problematic (structural vibrations).
Several factors influence resonant frequency:
For undamped systems, resonant frequency and natural frequency are the same. Natural frequency is the frequency at which a system oscillates when disturbed. Resonant frequency is the frequency at which maximum response occurs when driven by an external force. In lightly damped systems, they are essentially identical.
Light damping has minimal effect on the resonant frequency itself, but it reduces the amplitude at resonance. Heavy damping can shift the resonant frequency slightly lower. The quality factor (Q) describes how sharp the resonance peak is - higher Q means less damping and a sharper resonance.
No, resonant frequency is always positive. It represents a physical oscillation frequency, which must be a positive value. If you get a negative or imaginary result, check your input values for errors.
At resonance, the system oscillates with maximum amplitude. For LC circuits, this means maximum energy transfer between the inductor and capacitor. For mechanical systems, this means maximum displacement or velocity. Resonance can be useful (tuning, filtering) or problematic (vibrations, structural failure).
To increase resonant frequency, decrease either the inductance or capacitance (or both). To decrease resonant frequency, increase either the inductance or capacitance. The relationship is f ∝ 1/√(LC), so changing L or C by a factor of 4 changes frequency by a factor of 2.
For LC circuits, use consistent units: H and F for base units, or use common units like μH and μF. For mechanical systems, use N/m for spring constant and kg for mass (or convert to these). Frequency is typically in Hz, but kHz, MHz, or GHz may be more convenient for high frequencies.
Understanding resonant frequency is fundamental to electronics, mechanics, and wave physics. Our Resonant Frequency Calculator simplifies these calculations, supporting both LC circuits and mechanical systems with multiple unit conversions to make solving resonance problems easy and accurate.
Ready to explore more physics concepts? Check out our Frequency Calculator for general frequency calculations, our Wavelength Calculator for wave properties, or our Wavelength to Frequency Calculator for electromagnetic wave calculations.
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