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

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

✖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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✖Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.ⓘ Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) [f]

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

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = 0.571/(sqrt(Static Deflection))
f = 0.571/(sqrt(δ))
This formula uses 1 Functions, 2 Variables

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

Frequency - (Measured in Hertz) - Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.
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

f = 0.571/(sqrt(δ)) --> 0.571/(sqrt(0.072))

Evaluating ... ...

f = 2.1279913585873

STEP 3: Convert Result to Output's Unit

2.1279913585873 Hertz --> No Conversion Required

FINAL ANSWER

2.1279913585873 ≈ 2.127991 Hertz <-- 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 » Natural 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

LaTeX 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)

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

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

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

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

LaTeX Go Static Deflection = (0.571/Frequency)^2

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

LaTeX Go

Frequency = 0.571/(sqrt(Static Deflection))
f = 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 Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculator uses Frequency = 0.571/(sqrt(Static Deflection)) to calculate the Frequency, Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the frequency at which a shaft with a fixed end and uniformly distributed load vibrates freely in a transverse direction, providing insight into the shaft's natural frequency of vibration. Frequency is denoted by f symbol.

How to calculate Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) using this online calculator? To use this online calculator for Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load), enter Static Deflection (δ) and hit the calculate button. Here is how the Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculation can be explained with given input values -> 2.127991 = 0.571/(sqrt(0.072)).

FAQ

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

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the frequency at which a shaft with a fixed end and uniformly distributed load vibrates freely in a transverse direction, providing insight into the shaft's natural frequency of vibration and is represented as f = 0.571/(sqrt(δ)) or Frequency = 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 Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) formula is defined as a measure of the frequency at which a shaft with a fixed end and uniformly distributed load vibrates freely in a transverse direction, providing insight into the shaft's natural frequency of vibration is calculated using Frequency = 0.571/(sqrt(Static Deflection)). To calculate Natural 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 Frequency?

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

Frequency = 3.573*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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