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Circular Frequency given Static Deflection Calculator

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Uniformly Distributed Load Acting Over a Simply Supported Shaft General Shaft Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Shaft Subjected to a Number of Point Loads

✖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 [ω_n]

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Circular Frequency given Static Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))
ω_n = 2*pi*0.5615/(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*0.5615/(sqrt(δ)) --> 2*pi*0.5615/(sqrt(0.072))

Evaluating ... ...

ω_n = 13.1481115715979

STEP 3: Convert Result to Output's Unit

13.1481115715979 Radian per Second --> No Conversion Required

FINAL ANSWER

13.1481115715979 ≈ 13.14811 Radian per Second <-- Natural Circular Frequency

(Calculation completed in 00.020 seconds)

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< Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of Shaft given Static Deflection

LaTeX Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)

Uniformly Distributed Load Unit Length given Static Deflection

LaTeX Go Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)

Circular Frequency given Static Deflection

LaTeX Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

Natural Frequency given Static Deflection

LaTeX Go Frequency = 0.5615/(sqrt(Static Deflection))

Circular Frequency given Static Deflection Formula

LaTeX Go

Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))
ω_n = 2*pi*0.5615/(sqrt(δ))

What is Transverse and Longitudinal Vibration?

The difference between transverse and longitudinal waves is the direction in which the waves shake. If the wave shakes perpendicular to the movement direction, it's a transverse wave, if it shakes in the movement direction, then it's a longitudinal wave.

How to Calculate Circular Frequency given Static Deflection?

Circular Frequency given Static Deflection calculator uses Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection)) to calculate the Natural Circular Frequency, Circular Frequency given Static Deflection formula is defined as a measure of the natural frequency of free transverse vibrations in a system, providing insight into the oscillatory behavior of a structure under external forces, with applications in mechanical and civil engineering. Natural Circular Frequency is denoted by ω_n symbol.

How to calculate Circular Frequency given Static Deflection using this online calculator? To use this online calculator for Circular Frequency given Static Deflection, enter Static Deflection (δ) and hit the calculate button. Here is how the Circular Frequency given Static Deflection calculation can be explained with given input values -> 13.14811 = 2*pi*0.5615/(sqrt(0.072)).

FAQ

What is Circular Frequency given Static Deflection?

Circular Frequency given Static Deflection formula is defined as a measure of the natural frequency of free transverse vibrations in a system, providing insight into the oscillatory behavior of a structure under external forces, with applications in mechanical and civil engineering and is represented as ω_n = 2*pi*0.5615/(sqrt(δ)) or Natural Circular Frequency = 2*pi*0.5615/(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?

Circular Frequency given Static Deflection formula is defined as a measure of the natural frequency of free transverse vibrations in a system, providing insight into the oscillatory behavior of a structure under external forces, with applications in mechanical and civil engineering is calculated using Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection)). To calculate Circular Frequency given Static Deflection, 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 = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

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