Natural Frequency of Longitudinal Vibration Calculator

✖Stiffness of Constraint is the measure of resistance to deformation of a constraint in longitudinal and transverse vibrations due to inertia effects.ⓘ Stiffness of Constraint [s_constrain]			+10% -10%
✖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.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%
✖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.ⓘ Total Mass of Constraint [m_c]			+10% -10%

✖Frequency is the number of oscillations or cycles per second in a vibrating system, affected by inertia of constraint in longitudinal and transverse vibrations.ⓘ Natural Frequency of Longitudinal Vibration [f]

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Download Effect of Inertia of Constraint in Longitudinal and Transverse Vibrations Formulas PDF PDF Image

Natural Frequency of Longitudinal Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi)
f = sqrt((s_constrain)/(W_attached+m_c/3))*1/(2*pi)
This formula uses 1 Constants, 1 Functions, 4 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

Frequency - (Measured in Hertz) - Frequency is the number of oscillations or cycles per second in a vibrating system, affected by inertia of constraint in longitudinal and transverse vibrations.
Stiffness of Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the measure of resistance to deformation of a constraint in longitudinal and transverse vibrations due to inertia effects.
Load Attached to Free End of Constraint - (Measured in Kilogram) - 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.
Total Mass of Constraint - (Measured in Kilogram) - 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.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Constraint: 13 Newton per Meter --> 13 Newton per Meter No Conversion Required
Load Attached to Free End of Constraint: 0.52 Kilogram --> 0.52 Kilogram No Conversion Required
Total Mass of Constraint: 28.125 Kilogram --> 28.125 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = sqrt((s_constrain)/(W_attached+m_c/3))*1/(2*pi) --> sqrt((13)/(0.52+28.125/3))*1/(2*pi)

Evaluating ... ...

f = 0.182424812489929

STEP 3: Convert Result to Output's Unit

0.182424812489929 Hertz --> No Conversion Required

FINAL ANSWER

0.182424812489929 ≈ 0.182425 Hertz <-- Frequency

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Longitudinal Vibration Calculators

Velocity of Small Element for Longitudinal Vibration

LaTeX Go Velocity of Small Element = (Distance between Small Element and Fixed End*Longitudinal Velocity of Free End)/Length of Constraint

Longitudinal Velocity of Free End for Longitudinal Vibration

LaTeX Go Longitudinal Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass of Constraint)

Total Mass of Constraint for Longitudinal Vibration

LaTeX Go Total Mass of Constraint = (6*Kinetic Energy)/(Longitudinal Velocity of Free End^2)

Total Kinetic Energy of Constraint in Longitudinal Vibration

LaTeX Go Kinetic Energy = (Total Mass of Constraint*Longitudinal Velocity of Free End^2)/6

Natural Frequency of Longitudinal Vibration Formula

LaTeX Go

Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi)
f = sqrt((s_constrain)/(W_attached+m_c/3))*1/(2*pi)

What is Vibration?

Vibration is a repetitive, rhythmic movement of an object or system. It can be caused by a variety of factors, such as external forces, internal stresses, or natural frequencies. Vibrations can be beneficial or harmful, depending on the context. For example, vibrations in a musical instrument produce sound, while excessive vibrations in machinery can cause damage.

How to Calculate Natural Frequency of Longitudinal Vibration?

Natural Frequency of Longitudinal Vibration calculator uses Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi) to calculate 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 calculate Natural Frequency of Longitudinal Vibration using this online calculator? To use this online calculator 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. Here is how the Natural Frequency of Longitudinal Vibration calculation can be explained with given input values -> 0.18281 = sqrt((13)/(0.52+28.125/3))*1/(2*pi).

FAQ

What is Natural Frequency of Longitudinal Vibration?

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 and is represented as f = sqrt((s_constrain)/(W_attached+m_c/3))*1/(2*pi) or Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi). Stiffness of Constraint is the measure of resistance to deformation of a constraint in longitudinal and transverse vibrations due to inertia effects, 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 & 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.

How to calculate Natural Frequency of Longitudinal Vibration?

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 is calculated using Frequency = sqrt((Stiffness of Constraint)/(Load Attached to Free End of Constraint+Total Mass of Constraint/3))*1/(2*pi). To calculate Natural Frequency of Longitudinal Vibration, you need Stiffness of Constraint (s_constrain), Load Attached to Free End of Constraint (W_attached) & Total Mass of Constraint (m_c). With our tool, you need to enter the respective value for Stiffness of Constraint, Load Attached to Free End of Constraint & Total Mass of Constraint and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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