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Natural Frequency given Static Deflection 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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✖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 [f]

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Natural Frequency given Static Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = 0.5615/(sqrt(Static Deflection))
f = 0.5615/(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 = 0.5615/(sqrt(δ)) --> 0.5615/(sqrt(0.072))

Evaluating ... ...

f = 2.09258694894355

STEP 3: Convert Result to Output's Unit

2.09258694894355 Hertz --> No Conversion Required

FINAL ANSWER

2.09258694894355 ≈ 2.092587 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 » Uniformly Distributed Load Acting Over a Simply Supported Shaft » Natural Frequency given Static Deflection

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National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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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))

Natural Frequency given Static Deflection Formula

LaTeX Go

Frequency = 0.5615/(sqrt(Static Deflection))
f = 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 Natural Frequency given Static Deflection?

Natural Frequency given Static Deflection calculator uses Frequency = 0.5615/(sqrt(Static Deflection)) to calculate the Frequency, Natural Frequency given Static Deflection formula is defined as a measure of the frequency at which a system vibrates freely when displaced from its equilibrium position, providing insight into the dynamic behavior of structures and mechanical systems under various loads. Frequency is denoted by f symbol.

How to calculate Natural Frequency given Static Deflection using this online calculator? To use this online calculator for Natural Frequency given Static Deflection, enter Static Deflection (δ) and hit the calculate button. Here is how the Natural Frequency given Static Deflection calculation can be explained with given input values -> 2.092587 = 0.5615/(sqrt(0.072)).

FAQ

What is Natural Frequency given Static Deflection?

Natural Frequency given Static Deflection formula is defined as a measure of the frequency at which a system vibrates freely when displaced from its equilibrium position, providing insight into the dynamic behavior of structures and mechanical systems under various loads and is represented as f = 0.5615/(sqrt(δ)) or Frequency = 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 Natural Frequency given Static Deflection?

Natural Frequency given Static Deflection formula is defined as a measure of the frequency at which a system vibrates freely when displaced from its equilibrium position, providing insight into the dynamic behavior of structures and mechanical systems under various loads is calculated using Frequency = 0.5615/(sqrt(Static Deflection)). To calculate Natural 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 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 = 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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