Natural Frequency Calculator

What Is Natural Frequency?

Natural frequency is the rate at which a system oscillates when disturbed and left to vibrate freely. Every spring, pendulum, and structural beam has characteristic natural frequencies that engineers must account for to avoid resonance failures.

Spring-Mass System

$$f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

$k$ is the spring constant in newtons per meter and $m$ is the attached mass in kilograms. The angular frequency is $\omega = \sqrt{k/m}$ rad/s.

Simple Pendulum

$$f_n = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$$

$g$ is gravitational acceleration and $L$ is pendulum length. This formula applies for small oscillation angles where the bob follows simple harmonic motion.

Engineering Relevance

If an external force drives a system at its natural frequency, resonance can amplify vibrations dramatically. Related tools: Pendulum Calculator and Harmonic Wave Equation Calculator.

Frequently Asked Questions

What is the difference between natural and resonant frequency?

Natural frequency is the free vibration rate with no external driving force. Resonant frequency is the driving frequency that maximizes response, which equals the natural frequency for lightly damped systems.

How do I convert Hz to rad/s?

Multiply frequency in hertz by 2π. For example, 1.80 Hz equals 11.31 rad/s.

Does pendulum mass affect frequency?

For a simple pendulum, mass does not affect natural frequency. Only length and gravity matter for small angles.

What spring constant gives 2 Hz with 0.5 kg?

Rearrange fn = (1/2π)√(k/m) to get k = 4π²mfn². For 2 Hz and 0.5 kg, k ≈ 79 N/m.

Can natural frequency change?

Yes. Changing mass, stiffness, length, or support conditions shifts the natural frequency. Temperature and material properties also have small effects.

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What Is Natural Frequency?

Spring-Mass System

Simple Pendulum

Engineering Relevance

Frequently Asked Questions

Related Tools

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