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Natural Frequency of Each Cable Formula

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Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force. Check FAQs

ω n = (\frac{n}{π \cdot L span}) \cdot \sqrt{T \cdot \frac{[g]}{q}}

ω_n - Natural Frequency?n - Fundamental Vibration Mode?L_span - Cable Span?T - Cable Tension?q - Uniformly Distributed Load?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Natural Frequency of Each Cable Example

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Here is how the Natural Frequency of Each Cable equation looks like with Values.

Here is how the Natural Frequency of Each Cable equation looks like with Units.

Here is how the Natural Frequency of Each Cable equation looks like.

5.096 = (\frac{9.9}{3.1416 \cdot 15}) \cdot \sqrt{600 \cdot \frac{9.8066}{10}}

5.096Hz = (\frac{9.9}{3.1416 \cdot 15m}) \cdot \sqrt{600kN \cdot \frac{9.8066m/s²}{10kN/m}}

5.096 = (\frac{9.9}{3.1416 \cdot 15}) \cdot \sqrt{600 \cdot \frac{9.8066}{10}}

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Natural Frequency of Each Cable Solution

Follow our step by step solution on how to calculate Natural Frequency of Each Cable?

FIRST Step Consider the formula

ω n = (\frac{n}{π \cdot L span}) \cdot \sqrt{T \cdot \frac{[g]}{q}}

Next Step Substitute values of Variables

∴

ω n = (\frac{9.9}{π \cdot 15m}) \cdot \sqrt{600kN \cdot \frac{[g]}{10kN/m}}

Next Step Substitute values of Constants

∴

ω n = (\frac{9.9}{3.1416 \cdot 15m}) \cdot \sqrt{600kN \cdot \frac{9.8066m/s²}{10kN/m}}

Next Step Convert Units

∴

ω n = (\frac{9.9}{3.1416 \cdot 15m}) \cdot \sqrt{600000N \cdot \frac{9.8066m/s²}{10000N/m}}

Next Step Prepare to Evaluate

∴

ω n = (\frac{9.9}{3.1416 \cdot 15}) \cdot \sqrt{600000 \cdot \frac{9.8066}{10000}}

Next Step Evaluate

∴

ω n = 5.0960071166705Hz

LAST Step Rounding Answer

∴

ω n = 5.096Hz

Natural Frequency of Each Cable Formula Elements

Variables

Constants

Functions

Natural Frequency

Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.

Symbol: ω_n

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Natural Frequency

Fundamental Vibration Mode

Fundamental Vibration Mode is integral value denoting the mode of vibration.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Fundamental Vibration Mode

Cable Span

Cable Span is total length of cable in horizontal direction.

Symbol: L_span

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cable Span

Cable Tension

Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered).

Symbol: T

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Cable Tension

Uniformly Distributed Load

Uniformly distributed Load (UDL) is a load that is distributed or spread across the whole region of an element whose magnitude of the load remains uniform throughout the whole element.

Symbol: q

Measurement: Surface TensionUnit: kN/m

Note: Value can be positive or negative.

Formulas to find Uniformly Distributed Load

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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 in Cable Systems category

Go Span of Cable given Natural Frequency of Each Cable

L span = (\frac{n}{π \cdot ω n}) \cdot \sqrt{T \cdot (\frac{[g]}{q})}

Go Cable Tension using Natural Frequency of Each Cable

T = ({(ω n \cdot \frac{L span}{n} \cdot π)}^{2}) \cdot \frac{q}{[g]}

Go Fundamental Vibration Mode given Natural Frequency of Each Cable

n = \frac{ω n \cdot π \cdot L span}{\sqrt{T}} \cdot \sqrt{\frac{q}{[g]}}

How to Evaluate Natural Frequency of Each Cable?

Natural Frequency of Each Cable evaluator uses Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load) to evaluate the Natural Frequency, The Natural Frequency of Each Cable formula is defined as the frequency at which the system will vibrate when loaded with dynamic load. Natural Frequency is denoted by ω_n symbol.

How to evaluate Natural Frequency of Each Cable using this online evaluator? To use this online evaluator for Natural Frequency of Each Cable, enter Fundamental Vibration Mode (n), Cable Span (L_span), Cable Tension (T) & Uniformly Distributed Load (q) and hit the calculate button.

FAQs on Natural Frequency of Each Cable

What is the formula to find Natural Frequency of Each Cable?

The formula of Natural Frequency of Each Cable is expressed as Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load). Here is an example- 5.096007 = (9.9/(pi*15))*sqrt(600000*[g]/10000).

How to calculate Natural Frequency of Each Cable?

With Fundamental Vibration Mode (n), Cable Span (L_span), Cable Tension (T) & Uniformly Distributed Load (q) we can find Natural Frequency of Each Cable using the formula - Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Square Root Function function(s).

Can the Natural Frequency of Each Cable be negative?

No, the Natural Frequency of Each Cable, measured in Frequency cannot be negative.

Which unit is used to measure Natural Frequency of Each Cable?

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

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Natural Frequency of Each Cable Formula

Natural Frequency of Each Cable Example

Natural Frequency of Each Cable Solution

Natural Frequency of Each Cable Formula Elements

Other formulas in Cable Systems category

How to Evaluate Natural Frequency of Each Cable?

FAQs on Natural Frequency of Each Cable

Variable Name