Static Deflection given Natural Frequency Calculator

✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.ⓘ Frequency [f]			+10% -10%

✖Static deflection is the extension or compression of the constraint.ⓘ Static Deflection given Natural Frequency [δ]

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Formula

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Static Deflection given Natural Frequency

Formula

`"δ" = ("g")/((2*pi*"f")^2)`

Example

`"3.1E^-5m"=("9.8m/s²")/((2*pi*"90Hz")^2)`

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Download Natural Frequency of Free Longitudinal Vibrations Formula PDF

Static Deflection given Natural Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2)
δ = (g)/((2*pi*f)^2)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Frequency - (Measured in Hertz) - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.

STEP 1: Convert Input(s) to Base Unit

Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Frequency: 90 Hertz --> 90 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (g)/((2*pi*f)^2) --> (9.8)/((2*pi*90)^2)

Evaluating ... ...

δ = 3.06465308547812E-05

STEP 3: Convert Result to Output's Unit

3.06465308547812E-05 Meter --> No Conversion Required

FINAL ANSWER

3.06465308547812E-05 ≈ 3.1E-5 Meter <-- Static Deflection

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Longitudinal Vibrations » Equilibrium Method » Static Deflection given Natural Frequency

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< 12 Equilibrium Method Calculators

Load Attached to Free End of Constraint

Go Weight of Body in Newtons = (Static Deflection*Young's Modulus*Cross Sectional Area)/Length of Constraint

Length of Constraint

Go Length of Constraint = (Static Deflection*Young's Modulus*Cross Sectional Area)/Weight of Body in Newtons

Restoring Force using Weight of Body

Go Force = Weight of Body in Newtons-Stiffness of Constraint*(Static Deflection+Displacement of Body)

Acceleration of Body given Stiffness of Constraint

Go Acceleration of Body = (-Stiffness of Constraint*Displacement of Body)/Load Attached to Free End of Constraint

Displacement of Body given Stiffness of Constraint

Go Displacement of Body = (-Load Attached to Free End of Constraint*Acceleration of Body)/Stiffness of Constraint

Time Period of Free Longitudinal Vibrations

Go Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)

Angular Velocity of Free Longitudinal Vibrations

Go Natural Circular Frequency = sqrt(Stiffness of Constraint/Mass suspended from spring)

Critical Damping Coefficient given Spring Constant

Go Critical Damping Coefficient = 2*sqrt(Spring Constant/Mass suspended from spring)

Static Deflection given Natural Frequency

Go Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2)

Gravitational Pull Balanced by Spring Force

Go Weight of Body in Newtons = Stiffness of Constraint*Static Deflection

Restoring Force

Go Force = -Stiffness of Constraint*Displacement of Body

Young's Modulus

Go Young's Modulus = Stress/Strain

Static Deflection given Natural Frequency Formula

Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2)
δ = (g)/((2*pi*f)^2)

What is difference between longitudinal and transverse wave?

Transverse waves are always characterized by particle motion being perpendicular to wave motion. A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves.

How to Calculate Static Deflection given Natural Frequency?

Static Deflection given Natural Frequency calculator uses Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2) to calculate the Static Deflection, The Static Deflection given Natural Frequency formula is defined by dividing the acceleration due to gravity by the square of two times pi times the frequency. Static Deflection is denoted by δ symbol.

How to calculate Static Deflection given Natural Frequency using this online calculator? To use this online calculator for Static Deflection given Natural Frequency, enter Acceleration due to Gravity (g) & Frequency (f) and hit the calculate button. Here is how the Static Deflection given Natural Frequency calculation can be explained with given input values -> 3.1E-5 = (9.8)/((2*pi*90)^2).

FAQ

What is Static Deflection given Natural Frequency?

The Static Deflection given Natural Frequency formula is defined by dividing the acceleration due to gravity by the square of two times pi times the frequency and is represented as δ = (g)/((2*pi*f)^2) or Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2). Acceleration due to Gravity is acceleration gained by an object because of gravitational force & Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.

How to calculate Static Deflection given Natural Frequency?

The Static Deflection given Natural Frequency formula is defined by dividing the acceleration due to gravity by the square of two times pi times the frequency is calculated using Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2). To calculate Static Deflection given Natural Frequency, you need Acceleration due to Gravity (g) & Frequency (f). With our tool, you need to enter the respective value for Acceleration due to Gravity & Frequency 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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