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Span of Cable given Natural Frequency of Each Cable Formula

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Cable Span is total length of cable in horizontal direction. Check FAQs

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

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

Span of Cable given Natural Frequency of Each Cable Example

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

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

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

14.9883 = (\frac{9.9}{3.1416 \cdot 5.1}) \cdot \sqrt{600 \cdot (\frac{9.8066}{10})}

14.9883m = (\frac{9.9}{3.1416 \cdot 5.1Hz}) \cdot \sqrt{600kN \cdot (\frac{9.8066m/s²}{10kN/m})}

14.9883 = (\frac{9.9}{3.1416 \cdot 5.1}) \cdot \sqrt{600 \cdot (\frac{9.8066}{10})}

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Span of Cable given Natural Frequency of Each Cable Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L span = (\frac{9.9}{π \cdot 5.1Hz}) \cdot \sqrt{600kN \cdot (\frac{[g]}{10kN/m})}

Next Step Substitute values of Constants

∴

L span = (\frac{9.9}{3.1416 \cdot 5.1Hz}) \cdot \sqrt{600kN \cdot (\frac{9.8066m/s²}{10kN/m})}

Next Step Convert Units

∴

L span = (\frac{9.9}{3.1416 \cdot 5.1Hz}) \cdot \sqrt{600000N \cdot (\frac{9.8066m/s²}{10000N/m})}

Next Step Prepare to Evaluate

∴

L span = (\frac{9.9}{3.1416 \cdot 5.1}) \cdot \sqrt{600000 \cdot (\frac{9.8066}{10000})}

Next Step Evaluate

∴

L span = 14.9882562255015m

LAST Step Rounding Answer

∴

L span = 14.9883m

Span of Cable given Natural Frequency of Each Cable Formula Elements

Variables

Constants

Functions

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

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 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 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 Span of Cable given Natural Frequency of Each Cable?

Span of Cable given Natural Frequency of Each Cable evaluator uses Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load)) to evaluate the Cable Span, The Span of Cable given Natural Frequency of Each Cable formula is defined as the total length in the horizontal direction. Cable Span is denoted by L_span symbol.

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

FAQs on Span of Cable given Natural Frequency of Each Cable

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

The formula of Span of Cable given Natural Frequency of Each Cable is expressed as Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load)). Here is an example- 14.98826 = (9.9/(pi*5.1))*sqrt(600000*([g]/10000)).

How to calculate Span of Cable given Natural Frequency of Each Cable?

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

Can the Span of Cable given Natural Frequency of Each Cable be negative?

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

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

Span of Cable given Natural Frequency of Each Cable is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Span of Cable given Natural Frequency of Each Cable can be measured.

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Span of Cable given Natural Frequency of Each Cable Formula

Span of Cable given Natural Frequency of Each Cable Example

Span of Cable given Natural Frequency of Each Cable Solution

Span of Cable given Natural Frequency of Each Cable Formula Elements

Other formulas in Cable Systems category

How to Evaluate Span of Cable given Natural Frequency of Each Cable?

FAQs on Span of Cable given Natural Frequency of Each Cable

Variable Name