Circular Frequency given Static Deflection Calculator

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 a scalar measure of rotation rate.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.

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 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< 17 Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Static Deflection at Distance x from End A

Go Static deflection at distance x from end A = (Load per unit length*(Distance of small section of shaft from end A^4-2*Length of Shaft*Distance of small section of shaft from end A+Length of Shaft^3*Distance of small section of shaft from end A))/(24*Young's Modulus*Moment of inertia of shaft)

Natural Frequency due to Uniformly Distributed Load

Go Frequency = pi/2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

Circular Frequency due to Uniformly Distributed Load

Go 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))

Maximum Bending Moment at Distance x from End A

Go Bending Moment = (Load per unit length*Distance of small section of shaft from end A^2)/2-(Load per unit length*Length of Shaft*Distance of small section of shaft from end A)/2

Length of Shaft given Circular Frequency

Go Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)

Uniformly Distributed Load Unit Length given Circular Frequency

Go Load per unit length = (pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)

Moment of Inertia of Shaft given Circular Frequency

Go Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity)

Length of Shaft given Natural Frequency

Go Length of Shaft = ((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)

Uniformly Distributed Load Unit Length given Natural Frequency

Go Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)

Moment of Inertia of Shaft given Natural Frequency

Go Moment of inertia of shaft = (4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity)

Length of Shaft given Static Deflection

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

Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

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

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load

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

Uniformly Distributed Load Unit Length given Static Deflection

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

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

Natural Frequency given Static Deflection

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

Static Deflection using Natural Frequency

Go Static Deflection = (0.5615/Frequency)^2

Circular Frequency given Static Deflection Formula

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, The Circular Frequency given Static Deflection formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force. 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?

The Circular Frequency given Static Deflection formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force 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 extension or compression of the constraint.

How to calculate Circular Frequency given Static Deflection?

The Circular Frequency given Static Deflection formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force 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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