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Fundamental Vibration Mode given Natural Frequency of Each Cable Formula

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

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

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

Fundamental Vibration Mode given Natural Frequency of Each Cable Example

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Here is how the Fundamental Vibration Mode given Natural Frequency of Each Cable equation looks like with Values.

Here is how the Fundamental Vibration Mode given Natural Frequency of Each Cable equation looks like with Units.

Here is how the Fundamental Vibration Mode given Natural Frequency of Each Cable equation looks like.

9.9078 = \frac{5.1 \cdot 3.1416 \cdot 15}{\sqrt{600}} \cdot \sqrt{\frac{10}{9.8066}}

9.9078 = \frac{5.1Hz \cdot 3.1416 \cdot 15m}{\sqrt{600kN}} \cdot \sqrt{\frac{10kN/m}{9.8066m/s²}}

9.9078 = \frac{5.1 \cdot 3.1416 \cdot 15}{\sqrt{600}} \cdot \sqrt{\frac{10}{9.8066}}

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Fundamental Vibration Mode given Natural Frequency of Each Cable Solution

Follow our step by step solution on how to calculate Fundamental Vibration Mode given Natural Frequency of Each Cable?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

n = \frac{5.1Hz \cdot π \cdot 15m}{\sqrt{600kN}} \cdot \sqrt{\frac{10kN/m}{[g]}}

Next Step Substitute values of Constants

∴

n = \frac{5.1Hz \cdot 3.1416 \cdot 15m}{\sqrt{600kN}} \cdot \sqrt{\frac{10kN/m}{9.8066m/s²}}

Next Step Convert Units

∴

n = \frac{5.1Hz \cdot 3.1416 \cdot 15m}{\sqrt{600000N}} \cdot \sqrt{\frac{10000N/m}{9.8066m/s²}}

Next Step Prepare to Evaluate

∴

n = \frac{5.1 \cdot 3.1416 \cdot 15}{\sqrt{600000}} \cdot \sqrt{\frac{10000}{9.8066}}

Next Step Evaluate

∴

n = 9.90775696423828

LAST Step Rounding Answer

∴

n = 9.9078

Fundamental Vibration Mode given Natural Frequency of Each Cable Formula Elements

Variables

Constants

Functions

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

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

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 Natural Frequency of Each Cable

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

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]}

How to Evaluate Fundamental Vibration Mode given Natural Frequency of Each Cable?

Fundamental Vibration Mode given Natural Frequency of Each Cable evaluator uses Fundamental Vibration Mode = (Natural Frequency*pi*Cable Span)/sqrt(Cable Tension)*sqrt(Uniformly Distributed Load/[g]) to evaluate the Fundamental Vibration Mode, The Fundamental Vibration Mode given Natural Frequency of Each Cable formula is defined as the mode of vibration when dynamic load is applied. Fundamental Vibration Mode is denoted by n symbol.

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

FAQs on Fundamental Vibration Mode given Natural Frequency of Each Cable

What is the formula to find Fundamental Vibration Mode given Natural Frequency of Each Cable?

The formula of Fundamental Vibration Mode given Natural Frequency of Each Cable is expressed as Fundamental Vibration Mode = (Natural Frequency*pi*Cable Span)/sqrt(Cable Tension)*sqrt(Uniformly Distributed Load/[g]). Here is an example- 9.907757 = (5.1*pi*15)/sqrt(600000)*sqrt(10000/[g]).

How to calculate Fundamental Vibration Mode given Natural Frequency of Each Cable?

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

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Fundamental Vibration Mode given Natural Frequency of Each Cable Formula

Fundamental Vibration Mode given Natural Frequency of Each Cable Example

Fundamental Vibration Mode given Natural Frequency of Each Cable Solution

Fundamental Vibration Mode given Natural Frequency of Each Cable Formula Elements

Other formulas in Cable Systems category

How to Evaluate Fundamental Vibration Mode given Natural Frequency of Each Cable?

FAQs on Fundamental Vibration Mode given Natural Frequency of Each Cable

Variable Name