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Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Calculator

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✖Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.ⓘ Static Deflection [δ]

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✖Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.ⓘ Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) [ω_n]

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Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))
ω_n = (2*pi*0.571)/(sqrt(δ))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

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 Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.
Static Deflection - (Measured in Meter) - Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.

STEP 1: Convert Input(s) to Base Unit

Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_n = (2*pi*0.571)/(sqrt(δ)) --> (2*pi*0.571)/(sqrt(0.072))

Evaluating ... ...

ω_n = 13.3705640380808

STEP 3: Convert Result to Output's Unit

13.3705640380808 Radian per Second --> No Conversion Required

FINAL ANSWER

13.3705640380808 ≈ 13.37056 Radian per Second <-- Natural Circular Frequency

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Mechanical » Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load » Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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< Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

Go Moment of inertia of shaft = (Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

Go Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

Go Frequency = 0.571/(sqrt(Static Deflection))

Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Static Deflection = (0.571/Frequency)^2

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula

Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))
ω_n = (2*pi*0.571)/(sqrt(δ))

What is a Transverse Wave definition?

Transverse wave, motion in which all points on a wave oscillate along paths at right angles to the direction of the wave's advance. Surface ripples on water, seismic S (secondary) waves, and electromagnetic (e.g., radio and light) waves are examples of transverse waves.

How to Calculate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculator uses Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection)) to calculate the Natural Circular Frequency, Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the natural frequency of free transverse vibrations in a shaft under uniformly distributed load, fixed at both ends, which is essential in determining the dynamic behavior of the shaft. Natural Circular Frequency is denoted by ω_n symbol.

How to calculate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) using this online calculator? To use this online calculator for Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load), enter Static Deflection (δ) and hit the calculate button. Here is how the Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculation can be explained with given input values -> 13.37056 = (2*pi*0.571)/(sqrt(0.072)).

FAQ

What is Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the natural frequency of free transverse vibrations in a shaft under uniformly distributed load, fixed at both ends, which is essential in determining the dynamic behavior of the shaft and is represented as ω_n = (2*pi*0.571)/(sqrt(δ)) or Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection)). Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.

How to calculate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the natural frequency of free transverse vibrations in a shaft under uniformly distributed load, fixed at both ends, which is essential in determining the dynamic behavior of the shaft is calculated using Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection)). To calculate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load), you need Static Deflection (δ). With our tool, you need to enter the respective value for Static Deflection and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Natural Circular Frequency?

In this formula, Natural Circular Frequency uses Static Deflection. We can use 1 other way(s) to calculate the same, which is/are as follows -

Natural Circular Frequency = sqrt((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

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