🔊 Vibration Frequency Calculator

System Configuration

System Type

Unit System

Mass (m)

Stiffness (k)

Include Damping

Dark Mode

Educational Mode

Frequency Results

Natural Frequency (fₙ): - Hz

Angular Frequency (ωₙ): - rad/s

Period (T): - s

Damped Natural Frequency (fₙ): - Hz

Damping Ratio (ζ): -

Critical Damping (cₙ): -

Beam Properties

Moment of Inertia (I): -

Mass per Unit Length (μ): -

First Mode Frequency: - Hz

Second Mode Frequency: - Hz

Shaft Properties

Polar Moment of Inertia (J): -

Torsional Stiffness (kₜ): -

Natural Frequency: - Hz

Critical Speed: - RPM

Frequency Response

Phase Angle

Formula Breakdown

Select a system type and input parameters to see the formula breakdown.

System Visualization

Educational Guide

The natural frequency is the rate at which a system oscillates when not subjected to continuous or external forces.

For a simple mass-spring system: fₙ = (1/2π)√(k/m)

Damping reduces the amplitude of oscillations over time. Critical damping is the minimum amount needed to prevent oscillation.

Damping ratio: ζ = c/cₙ where cₙ = 2√(mk)

Beams vibrate at multiple natural frequencies corresponding to different mode shapes.

Cantilever beam: fₙ = (βₙ²/2π)√(EI/μL⁴) where β₁=1.875, β₂=4.694

Shafts experience torsional vibrations with natural frequencies dependent on material and geometry.

Torsional frequency: fₙ = (1/2π)√(kₜ/I) where kₜ = GJ/L

Vibration Frequency Calculator

System Configuration

Frequency Results

Beam Properties

Shaft Properties

Frequency Response

Phase Angle

Formula Breakdown

System Visualization

First Mode Shape

Second Mode Shape

Educational Guide

Export Results

Vibration Frequency Calculator

System Configuration

Frequency Results

Beam Properties

Shaft Properties

Frequency Response

Phase Angle

Formula Breakdown

System Visualization

First Mode Shape

Second Mode Shape

Educational Guide

Natural Frequency

Damping Effects

Beam Vibrations

Shaft Vibrations

Export Results