Static Deflection given Natural Frequency Calculator

✖Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, typically measured in m/s².ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Frequency is the number of oscillations or cycles per second of a free longitudinal vibration of an object or substance in a given time period.ⓘ Frequency [f]			+10% -10%

✖Static Deflection is the maximum displacement of an object or structure under a given load, in the context of natural frequency of free longitudinal vibrations.ⓘ Static Deflection given Natural Frequency [δ]

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Formula

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Static Deflection given Natural Frequency

Formula

δ = \frac{g}{{(2 \cdot π \cdot f)}^{2}}

Example

0.615629 m = \frac{9.8 m/s²}{{(2 \cdot π \cdot 0.635 Hz)}^{2}}

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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 maximum displacement of an object or structure under a given load, in the context of natural frequency of free longitudinal vibrations.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, typically measured in m/s².
Frequency - (Measured in Hertz) - Frequency is the number of oscillations or cycles per second of a free longitudinal vibration of an object or substance in a given time period.

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: 0.635 Hertz --> 0.635 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (g)/((2*pi*f)^2) --> (9.8)/((2*pi*0.635)^2)

Evaluating ... ...

δ = 0.61562874306833

STEP 3: Convert Result to Output's Unit

0.61562874306833 Meter --> No Conversion Required

FINAL ANSWER

0.61562874306833 ≈ 0.615629 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 » Mechanical » Equilibrium Method » Static Deflection given Natural Frequency

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National Institute Of Technology (NIT), Hamirpur

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< Equilibrium Method Calculators

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

Gravitational Pull Balanced by Spring Force

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

Restoring Force

Go Restoring Force = -Stiffness of Constraint*Displacement of Body

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, Static Deflection given Natural Frequency formula is defined as a measure of the maximum displacement of an object from its equilibrium position when subjected to a periodic force, providing insight into the oscillatory behavior of a system in free longitudinal vibrations. 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 -> 0.606047 = (9.8)/((2*pi*0.635)^2).

FAQ

What is Static Deflection given Natural Frequency?

Static Deflection given Natural Frequency formula is defined as a measure of the maximum displacement of an object from its equilibrium position when subjected to a periodic force, providing insight into the oscillatory behavior of a system in free longitudinal vibrations 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 the rate of change of velocity of an object under the influence of gravitational force, typically measured in m/s² & Frequency is the number of oscillations or cycles per second of a free longitudinal vibration of an object or substance in a given time period.

How to calculate Static Deflection given Natural Frequency?

Static Deflection given Natural Frequency formula is defined as a measure of the maximum displacement of an object from its equilibrium position when subjected to a periodic force, providing insight into the oscillatory behavior of a system in free longitudinal vibrations 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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