Natural Frequency of Each Cable Calculator

✖Fundamental Vibration Mode is integral value denoting the mode of vibration.ⓘ Fundamental Vibration Mode [n]			+10% -10%
✖Cable Span is total length of cable in horizontal direction.ⓘ Cable Span [L_span]			+10% -10%
✖Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered).ⓘ Cable Tension [T]			+10% -10%
✖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.ⓘ Uniformly Distributed Load [q]			+10% -10%

✖Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.ⓘ Natural Frequency of Each Cable [ω_n]

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Formula

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Natural Frequency of Each Cable

Formula

`"ω"_{"n"} = ("n"/(pi*"L"_{"span"}))*sqrt("T"*"[g]"/"q")`

Example

`"5.096007Hz"=("9.9"/(pi*"15m"))*sqrt("600kN"*"[g]"/"10.0kN/m")`

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Natural Frequency of Each Cable Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load)
ω_n = (n/(pi*L_span))*sqrt(T*[g]/q)
This formula uses 2 Constants, 1 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Natural Frequency - (Measured in Hertz) - Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.
Fundamental Vibration Mode - Fundamental Vibration Mode is integral value denoting the mode of vibration.
Cable Span - (Measured in Meter) - Cable Span is total length of cable in horizontal direction.
Cable Tension - (Measured in Newton) - Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered).
Uniformly Distributed Load - (Measured in Newton per Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Fundamental Vibration Mode: 9.9 --> No Conversion Required
Cable Span: 15 Meter --> 15 Meter No Conversion Required
Cable Tension: 600 Kilonewton --> 600000 Newton (Check conversion here)
Uniformly Distributed Load: 10 Kilonewton per Meter --> 10000 Newton per Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_n = (n/(pi*L_span))*sqrt(T*[g]/q) --> (9.9/(pi*15))*sqrt(600000*[g]/10000)

Evaluating ... ...

ω_n = 5.0960071166705

STEP 3: Convert Result to Output's Unit

5.0960071166705 Hertz --> No Conversion Required

FINAL ANSWER

5.0960071166705 ≈ 5.096007 Hertz <-- Natural Frequency

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

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< 4 Cable Systems Calculators

Fundamental Vibration Mode given Natural Frequency of Each Cable

Go Fundamental Vibration Mode = (Natural Frequency*pi*Cable Span)/sqrt(Cable Tension)*sqrt(Uniformly Distributed Load/[g])

Span of Cable given Natural Frequency of Each Cable

Go Cable Span = (Fundamental Vibration Mode/(pi*Natural Frequency))*sqrt(Cable Tension*([g]/Uniformly Distributed Load))

Natural Frequency of Each Cable

Go Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load)

Cable Tension using Natural Frequency of Each Cable

Go Cable Tension = ((Natural Frequency*Cable Span/Fundamental Vibration Mode*pi)^2)*Uniformly Distributed Load/[g]

Natural Frequency of Each Cable Formula

Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load)
ω_n = (n/(pi*L_span))*sqrt(T*[g]/q)

What is the natural frequency of a system?

Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving or damping force. The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all parts of the system move sinesuoidally with that same frequency).

How to Calculate Natural Frequency of Each Cable?

Natural Frequency of Each Cable calculator uses Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load) to calculate 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 calculate Natural Frequency of Each Cable using this online calculator? To use this online calculator 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. Here is how the Natural Frequency of Each Cable calculation can be explained with given input values -> 5.096007 = (9.9/(pi*15))*sqrt(600000*[g]/10000).

FAQ

What is Natural Frequency of Each Cable?

The Natural Frequency of Each Cable formula is defined as the frequency at which the system will vibrate when loaded with dynamic load and is represented as ω_n = (n/(pi*L_span))*sqrt(T*[g]/q) or Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load). Fundamental Vibration Mode is integral value denoting the mode of vibration, Cable Span is total length of cable in horizontal direction, Cable Tension is the tension on the cable or the structure at a particular point. (if any random points are considered) & 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.

How to calculate Natural Frequency of Each Cable?

The Natural Frequency of Each Cable formula is defined as the frequency at which the system will vibrate when loaded with dynamic load is calculated using Natural Frequency = (Fundamental Vibration Mode/(pi*Cable Span))*sqrt(Cable Tension*[g]/Uniformly Distributed Load). To calculate Natural Frequency of Each Cable, you need Fundamental Vibration Mode (n), Cable Span (L_span), Cable Tension (T) & Uniformly Distributed Load (q). With our tool, you need to enter the respective value for Fundamental Vibration Mode, Cable Span, Cable Tension & Uniformly Distributed Load and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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