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Static Deflection given Natural Frequency Formula

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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. Check FAQs

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

δ - Static Deflection?g - Acceleration due to Gravity?f - Frequency?π - Archimedes' constant?

Static Deflection given Natural Frequency Example

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Here is how the Static Deflection given Natural Frequency equation looks like with Values.

Here is how the Static Deflection given Natural Frequency equation looks like with Units.

Here is how the Static Deflection given Natural Frequency equation looks like.

0.6156 = \frac{9.8}{{(2 \cdot 3.1416 \cdot 0.635)}^{2}}

0.6156m = \frac{9.8m/s²}{{(2 \cdot 3.1416 \cdot 0.635Hz)}^{2}}

0.6156 = \frac{9.8}{{(2 \cdot 3.1416 \cdot 0.635)}^{2}}

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Static Deflection given Natural Frequency Solution

Follow our step by step solution on how to calculate Static Deflection given Natural Frequency?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

δ = \frac{9.8m/s²}{{(2 \cdot 3.1416 \cdot 0.635Hz)}^{2}}

Next Step Prepare to Evaluate

∴

δ = \frac{9.8}{{(2 \cdot 3.1416 \cdot 0.635)}^{2}}

Next Step Evaluate

∴

δ = 0.61562874306833m

LAST Step Rounding Answer

∴

δ = 0.6156m

Static Deflection given Natural Frequency Formula Elements

Variables

Constants

Static Deflection

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.

Symbol: δ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Static Deflection

Acceleration due to Gravity

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.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Frequency

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.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Frequency

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

Other formulas in Equilibrium Method category

Go Gravitational Pull Balanced by Spring Force

W = s constrain \cdot δ

Go Restoring Force

F re = - s constrain \cdot s body

Go Acceleration of Body given Stiffness of Constraint

a = \frac{s constrain \cdot s body}{W attached}

Go Displacement of Body given Stiffness of Constraint

s body = \frac{W attached \cdot a}{s constrain}

How to Evaluate Static Deflection given Natural Frequency?

Static Deflection given Natural Frequency evaluator uses Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2) to evaluate 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 evaluate Static Deflection given Natural Frequency using this online evaluator? To use this online evaluator for Static Deflection given Natural Frequency, enter Acceleration due to Gravity (g) & Frequency (f) and hit the calculate button.

FAQs on Static Deflection given Natural Frequency

What is the formula to find Static Deflection given Natural Frequency?

The formula of Static Deflection given Natural Frequency is expressed as Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2). Here is an example- 0.606047 = (9.8)/((2*pi*0.635)^2).

How to calculate Static Deflection given Natural Frequency?

With Acceleration due to Gravity (g) & Frequency (f) we can find Static Deflection given Natural Frequency using the formula - Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2). This formula also uses Archimedes' constant .

Can the Static Deflection given Natural Frequency be negative?

No, the Static Deflection given Natural Frequency, measured in Length cannot be negative.

Which unit is used to measure Static Deflection given Natural Frequency?

Static Deflection given Natural Frequency is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Static Deflection given Natural Frequency can be measured.

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