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Frequency of Damped Vibration Formula

GoFrequency of Damped Vibration using Natural Frequency Formula

GoFrequency of Undamped Vibration Formula

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Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second. Check FAQs

f = \frac{1}{2 \cdot π} \cdot \sqrt{\frac{k}{m} - {(\frac{c}{2 \cdot m})}^{2}}

f - Frequency?k - Stiffness of Spring?m - Mass Suspended from Spring?c - Damping Coefficient?π - Archimedes' constant?

Frequency of Damped Vibration Example

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Here is how the Frequency of Damped Vibration equation looks like with Values.

Here is how the Frequency of Damped Vibration equation looks like with Units.

Here is how the Frequency of Damped Vibration equation looks like.

1.1015 = \frac{1}{2 \cdot 3.1416} \cdot \sqrt{\frac{60}{1.25} - {(\frac{0.8}{2 \cdot 1.25})}^{2}}

1.1015Hz = \frac{1}{2 \cdot 3.1416} \cdot \sqrt{\frac{60N/m}{1.25kg} - {(\frac{0.8Ns/m}{2 \cdot 1.25kg})}^{2}}

1.1015 = \frac{1}{2 \cdot 3.1416} \cdot \sqrt{\frac{60}{1.25} - {(\frac{0.8}{2 \cdot 1.25})}^{2}}

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Frequency of Damped Vibration Solution

Follow our step by step solution on how to calculate Frequency of Damped Vibration?

FIRST Step Consider the formula

f = \frac{1}{2 \cdot π} \cdot \sqrt{\frac{k}{m} - {(\frac{c}{2 \cdot m})}^{2}}

Next Step Substitute values of Variables

∴

f = \frac{1}{2 \cdot π} \cdot \sqrt{\frac{60N/m}{1.25kg} - {(\frac{0.8Ns/m}{2 \cdot 1.25kg})}^{2}}

Next Step Substitute values of Constants

∴

f = \frac{1}{2 \cdot 3.1416} \cdot \sqrt{\frac{60N/m}{1.25kg} - {(\frac{0.8Ns/m}{2 \cdot 1.25kg})}^{2}}

Next Step Prepare to Evaluate

∴

f = \frac{1}{2 \cdot 3.1416} \cdot \sqrt{\frac{60}{1.25} - {(\frac{0.8}{2 \cdot 1.25})}^{2}}

Next Step Evaluate

∴

f = 1.10148099457358Hz

LAST Step Rounding Answer

∴

f = 1.1015Hz

Frequency of Damped Vibration Formula Elements

Variables

Constants

Functions

Frequency

Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Frequency

Stiffness of Spring

Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.

Symbol: k

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Spring

Mass Suspended from Spring

A Mass Suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass Suspended from Spring

Damping Coefficient

Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.

Symbol: c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value can be positive or negative.

Formulas to find Damping Coefficient

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 to find Frequency

Go Frequency of Damped Vibration using Natural Frequency

f = \frac{1}{2 \cdot π} \cdot \sqrt{{ω n}^{2} - a^{2}}

Go Frequency of Undamped Vibration

f = \frac{1}{2 \cdot π} \cdot \sqrt{\frac{k}{m}}

Other formulas in Frequency of Free Damped Vibrations category

Go Condition for Critical Damping

c c = 2 \cdot m \cdot \sqrt{\frac{k}{m}}

Go Critical Damping Coefficient

c c = 2 \cdot m \cdot ω n

Go Damping Factor

ζ = \frac{c}{c c}

Go Damping Factor given Natural Frequency

ζ = \frac{c}{2 \cdot m \cdot ω n}

How to Evaluate Frequency of Damped Vibration?

Frequency of Damped Vibration evaluator uses Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2) to evaluate the Frequency, Frequency of Damped Vibration formula is defined as a measure of the number of oscillations per unit time of an object experiencing a damping force, which opposes its motion, in a vibrating system, providing insight into the system's energy loss and stability. Frequency is denoted by f symbol.

How to evaluate Frequency of Damped Vibration using this online evaluator? To use this online evaluator for Frequency of Damped Vibration, enter Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c) and hit the calculate button.

FAQs on Frequency of Damped Vibration

What is the formula to find Frequency of Damped Vibration?

The formula of Frequency of Damped Vibration is expressed as Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2). Here is an example- 1.101481 = 1/(2*pi)*sqrt(60/1.25-(0.8/(2*1.25))^2).

How to calculate Frequency of Damped Vibration?

With Stiffness of Spring (k), Mass Suspended from Spring (m) & Damping Coefficient (c) we can find Frequency of Damped Vibration using the formula - Frequency = 1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring-(Damping Coefficient/(2*Mass Suspended from Spring))^2). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Frequency?

Here are the different ways to Calculate Frequency-

Frequency=1/(2*pi)*sqrt(Natural Circular Frequency^2-Frequency Constant for Calculation^2)
Frequency=1/(2*pi)*sqrt(Stiffness of Spring/Mass Suspended from Spring)

Can the Frequency of Damped Vibration be negative?

Yes, the Frequency of Damped Vibration, measured in Frequency can be negative.

Which unit is used to measure Frequency of Damped Vibration?

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

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