Fundamental Vibration Mode given Natural Frequency of Each Cable Calculator

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

✖Fundamental Vibration Mode is integral value denoting the mode of vibration.ⓘ Fundamental Vibration Mode given Natural Frequency of Each Cable [n]

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Fundamental Vibration Mode given Natural Frequency of Each Cable Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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

Natural Frequency: 5.1 Hertz --> 5.1 Hertz 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

n = (ω_n*pi*L_span)/sqrt(T)*sqrt(q/[g]) --> (5.1*pi*15)/sqrt(600000)*sqrt(10000/[g])

Evaluating ... ...

n = 9.90775696423828

STEP 3: Convert Result to Output's Unit

9.90775696423828 --> No Conversion Required

FINAL ANSWER

9.90775696423828 ≈ 9.907757 <-- Fundamental Vibration Mode

(Calculation completed in 00.020 seconds)

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< Cable Systems Calculators

Fundamental Vibration Mode given Natural Frequency of Each Cable

LaTeX 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

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

Natural Frequency of Each Cable

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

Cable Tension using Natural Frequency of Each Cable

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

Fundamental Vibration Mode given Natural Frequency of Each Cable Formula

LaTeX Go

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

What is Dynamic Load?

Dynamic load is the load the actuator sees when it is powered and extending or retracting. The dynamic load capacity of an actuator refers to how much the actuator can push or pull.

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 Fundamental Vibration Mode given Natural Frequency of Each Cable?

Fundamental Vibration Mode given Natural Frequency of Each Cable calculator uses Fundamental Vibration Mode = (Natural Frequency*pi*Cable Span)/sqrt(Cable Tension)*sqrt(Uniformly Distributed Load/[g]) to calculate 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 calculate Fundamental Vibration Mode given Natural Frequency of Each Cable using this online calculator? To use this online calculator 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. Here is how the Fundamental Vibration Mode given Natural Frequency of Each Cable calculation can be explained with given input values -> 9.907757 = (5.1*pi*15)/sqrt(600000)*sqrt(10000/[g]).

FAQ

What is Fundamental Vibration Mode given Natural Frequency of Each Cable?

The Fundamental Vibration Mode given Natural Frequency of Each Cable formula is defined as the mode of vibration when dynamic load is applied and is represented as n = (ω_n*pi*L_span)/sqrt(T)*sqrt(q/[g]) or Fundamental Vibration Mode = (Natural Frequency*pi*Cable Span)/sqrt(Cable Tension)*sqrt(Uniformly Distributed Load/[g]). Natural Frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force, 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 Fundamental Vibration Mode given Natural Frequency of Each Cable?

The Fundamental Vibration Mode given Natural Frequency of Each Cable formula is defined as the mode of vibration when dynamic load is applied is calculated using Fundamental Vibration Mode = (Natural Frequency*pi*Cable Span)/sqrt(Cable Tension)*sqrt(Uniformly Distributed Load/[g]). To calculate Fundamental Vibration Mode given Natural Frequency of Each Cable, you need Natural Frequency (ω_n), Cable Span (L_span), Cable Tension (T) & Uniformly Distributed Load (q). With our tool, you need to enter the respective value for Natural Frequency, 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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