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Resonant Frequency Formula

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Resonant Frequency is the oscillation of a system at its natural or unforced resonance. Check FAQs

ω r = ω n \cdot \sqrt{1 - 2 \cdot ζ^{2}}

ω_r - Resonant Frequency?ω_n - Natural Frequency of Oscillation?ζ - Damping Ratio?

Resonant Frequency Example

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With units

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Here is how the Resonant Frequency equation looks like with Values.

Here is how the Resonant Frequency equation looks like with Units.

Here is how the Resonant Frequency equation looks like.

22.7688 = 23 \cdot \sqrt{1 - 2 \cdot {0.1}^{2}}

22.7688Hz = 23Hz \cdot \sqrt{1 - 2 \cdot {0.1}^{2}}

22.7688 = 23 \cdot \sqrt{1 - 2 \cdot {0.1}^{2}}

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Resonant Frequency Solution

Follow our step by step solution on how to calculate Resonant Frequency?

FIRST Step Consider the formula

ω r = ω n \cdot \sqrt{1 - 2 \cdot ζ^{2}}

Next Step Substitute values of Variables

∴

ω r = 23Hz \cdot \sqrt{1 - 2 \cdot {0.1}^{2}}

Next Step Prepare to Evaluate

∴

ω r = 23 \cdot \sqrt{1 - 2 \cdot {0.1}^{2}}

Next Step Evaluate

∴

ω r = 22.7688383542068Hz

LAST Step Rounding Answer

∴

ω r = 22.7688Hz

Resonant Frequency Formula Elements

Variables

Functions

Resonant Frequency

Resonant Frequency is the oscillation of a system at its natural or unforced resonance.

Symbol: ω_r

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Resonant Frequency

Natural Frequency of Oscillation

The Natural Frequency of Oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position.

Symbol: ω_n

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Natural Frequency of Oscillation

Damping Ratio

Damping Ratio in control system is defined as the ratio with which any signal gets decayed.

Symbol: ζ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Damping Ratio

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Fundamental Parameters category

Go Damping Ratio or Damping Factor

ζ = \frac{c}{2 \cdot \sqrt{m \cdot K spring}}

Go Damped Natural Frequency

ω d = ω n \cdot \sqrt{1 - ζ^{2}}

Go Resonant Peak

M r = \frac{1}{2 \cdot ζ \cdot \sqrt{1 - ζ^{2}}}

Go Bandwidth Frequency given Damping Ratio

f b = ω n \cdot (\sqrt{1 - (2 \cdot ζ^{2})} + \sqrt{ζ^{4} - (4 \cdot ζ^{2}) + 2})

How to Evaluate Resonant Frequency?

Resonant Frequency evaluator uses Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2) to evaluate the Resonant Frequency, Resonant Frequency formula is defined as the frequency at which the magnitude of the frequency response has peak value for the first time. Resonant Frequency is denoted by ω_r symbol.

How to evaluate Resonant Frequency using this online evaluator? To use this online evaluator for Resonant Frequency, enter Natural Frequency of Oscillation (ω_n) & Damping Ratio (ζ) and hit the calculate button.

FAQs on Resonant Frequency

What is the formula to find Resonant Frequency?

The formula of Resonant Frequency is expressed as Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2). Here is an example- 22.76884 = 23*sqrt(1-2*0.1^2).

How to calculate Resonant Frequency?

With Natural Frequency of Oscillation (ω_n) & Damping Ratio (ζ) we can find Resonant Frequency using the formula - Resonant Frequency = Natural Frequency of Oscillation*sqrt(1-2*Damping Ratio^2). This formula also uses Square Root (sqrt) function(s).

Can the Resonant Frequency be negative?

No, the Resonant Frequency, measured in Frequency cannot be negative.

Which unit is used to measure Resonant Frequency?

Resonant Frequency is usually measured using the Hertz[Hz] for Frequency. Petahertz[Hz], Terahertz[Hz], Gigahertz[Hz] are the few other units in which Resonant Frequency can be measured.

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Resonant Frequency Formula

Resonant Frequency Example

Resonant Frequency Solution

Resonant Frequency Formula Elements

Other formulas in Fundamental Parameters category

How to Evaluate Resonant Frequency?

FAQs on Resonant Frequency

Variable Name