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Natural Frequency of Longitudinal Vibration Formula

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Frequency is the number of oscillations or cycles per second in a vibrating system, affected by inertia of constraint in longitudinal and transverse vibrations. Check FAQs

f = \sqrt{\frac{s constrain}{W attached + \frac{m c}{3}}} \cdot \frac{1}{2 \cdot π}

f - Frequency?s_constrain - Stiffness of Constraint?W_attached - Load Attached to Free End of Constraint?m_c - Total Mass of Constraint?π - Archimedes' constant?

Natural Frequency of Longitudinal Vibration Example

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Here is how the Natural Frequency of Longitudinal Vibration equation looks like with Values.

Here is how the Natural Frequency of Longitudinal Vibration equation looks like with Units.

Here is how the Natural Frequency of Longitudinal Vibration equation looks like.

0.1824 = \sqrt{\frac{13}{0.52 + \frac{28.125}{3}}} \cdot \frac{1}{2 \cdot 3.1416}

0.1824Hz = \sqrt{\frac{13N/m}{0.52kg + \frac{28.125kg}{3}}} \cdot \frac{1}{2 \cdot 3.1416}

0.1824 = \sqrt{\frac{13}{0.52 + \frac{28.125}{3}}} \cdot \frac{1}{2 \cdot 3.1416}

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Natural Frequency of Longitudinal Vibration Solution

Follow our step by step solution on how to calculate Natural Frequency of Longitudinal Vibration?

FIRST Step Consider the formula

f = \sqrt{\frac{s constrain}{W attached + \frac{m c}{3}}} \cdot \frac{1}{2 \cdot π}

Next Step Substitute values of Variables

∴

f = \sqrt{\frac{13N/m}{0.52kg + \frac{28.125kg}{3}}} \cdot \frac{1}{2 \cdot π}

Next Step Substitute values of Constants

∴

f = \sqrt{\frac{13N/m}{0.52kg + \frac{28.125kg}{3}}} \cdot \frac{1}{2 \cdot 3.1416}

Next Step Prepare to Evaluate

∴

f = \sqrt{\frac{13}{0.52 + \frac{28.125}{3}}} \cdot \frac{1}{2 \cdot 3.1416}

Next Step Evaluate

∴

f = 0.182424812489929Hz

LAST Step Rounding Answer

∴

f = 0.1824Hz

Natural Frequency of Longitudinal Vibration Formula Elements

Variables

Constants

Functions

Frequency

Frequency is the number of oscillations or cycles per second in a vibrating system, affected by inertia of constraint in longitudinal and transverse vibrations.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Frequency

Stiffness of Constraint

Stiffness of Constraint is the measure of resistance to deformation of a constraint in longitudinal and transverse vibrations due to inertia effects.

Symbol: s_constrain

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Constraint

Load Attached to Free End of Constraint

Load Attached to Free End of Constraint is the force exerted on the free end of a constraint in longitudinal and transverse vibrations due to inertia.

Symbol: W_attached

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Load Attached to Free End of Constraint

Total Mass of Constraint

Total Mass of Constraint is the total mass of the constraint that affects the longitudinal and transverse vibrations of an object due to its inertia.

Symbol: m_c

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Total Mass of Constraint

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other formulas in Longitudinal Vibration category

Go Velocity of Small Element for Longitudinal Vibration

v s = \frac{x \cdot V longitudinal}{l}

Go Total Kinetic Energy of Constraint in Longitudinal Vibration

KE = \frac{m c \cdot {V longitudinal}^{2}}{6}

Go Longitudinal Velocity of Free End for Longitudinal Vibration

V longitudinal = \sqrt{\frac{6 \cdot KE}{m c}}

Go Total Mass of Constraint for Longitudinal Vibration

m c = \frac{6 \cdot KE}{{V longitudinal}^{2}}

How to Evaluate Natural Frequency of Longitudinal Vibration?

Natural Frequency of Longitudinal Vibration evaluator uses Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi) to evaluate the Frequency, Natural Frequency of Longitudinal Vibration formula is defined as a measure of the frequency at which a system vibrates longitudinally when subjected to an external force, influenced by the stiffness of the constraint and the mass of the attached object, providing insight into the effect of inertia on longitudinal vibrations. Frequency is denoted by f symbol.

How to evaluate Natural Frequency of Longitudinal Vibration using this online evaluator? To use this online evaluator for Natural Frequency of Longitudinal Vibration, enter Stiffness of Constraint (s_constrain), Load Attached to Free End of Constraint (W_attached) & Total Mass of Constraint (m_c) and hit the calculate button.

FAQs on Natural Frequency of Longitudinal Vibration

What is the formula to find Natural Frequency of Longitudinal Vibration?

The formula of Natural Frequency of Longitudinal Vibration is expressed as Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi). Here is an example- 0.18281 = sqrt((13)/(0.52+28.125/3))*1/(2*pi).

How to calculate Natural Frequency of Longitudinal Vibration?

With Stiffness of Constraint (s_constrain), Load Attached to Free End of Constraint (W_attached) & Total Mass of Constraint (m_c) we can find Natural Frequency of Longitudinal Vibration using the formula - Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Natural Frequency of Longitudinal Vibration be negative?

No, the Natural Frequency of Longitudinal Vibration, measured in Frequency cannot be negative.

Which unit is used to measure Natural Frequency of Longitudinal Vibration?

Natural Frequency of Longitudinal Vibration is usually measured using the Hertz[Hz] for Frequency. Petahertz[Hz], Terahertz[Hz], Gigahertz[Hz] are the few other units in which Natural Frequency of Longitudinal Vibration can be measured.

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Natural Frequency of Longitudinal Vibration Formula

Natural Frequency of Longitudinal Vibration Example

Natural Frequency of Longitudinal Vibration Solution

Natural Frequency of Longitudinal Vibration Formula Elements

Other formulas in Longitudinal Vibration category

How to Evaluate Natural Frequency of Longitudinal Vibration?

FAQs on Natural Frequency of Longitudinal Vibration

Variable Name