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Maximum Displacement of Vibration given Transmissibility Ratio Formula

GoMaximum Displacement of Vibration using Force Transmitted Formula

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Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system. Check FAQs

K = \frac{ε \cdot F a}{\sqrt{k^{2} + {(c \cdot ω)}^{2}}}

K - Maximum Displacement?ε - Transmissibility Ratio?F_a - Applied Force?k - Stiffness of Spring?c - Damping Coefficient?ω - Angular Velocity?

Maximum Displacement of Vibration given Transmissibility Ratio Example

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Here is how the Maximum Displacement of Vibration given Transmissibility Ratio equation looks like with Values.

Here is how the Maximum Displacement of Vibration given Transmissibility Ratio equation looks like with Units.

Here is how the Maximum Displacement of Vibration given Transmissibility Ratio equation looks like.

0.8 = \frac{19.2086 \cdot 2500}{\sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}

0.8m = \frac{19.2086 \cdot 2500N}{\sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}

0.8 = \frac{19.2086 \cdot 2500}{\sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}

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Maximum Displacement of Vibration given Transmissibility Ratio Solution

Follow our step by step solution on how to calculate Maximum Displacement of Vibration given Transmissibility Ratio?

FIRST Step Consider the formula

K = \frac{ε \cdot F a}{\sqrt{k^{2} + {(c \cdot ω)}^{2}}}

Next Step Substitute values of Variables

∴

K = \frac{19.2086 \cdot 2500N}{\sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}

Next Step Prepare to Evaluate

∴

K = \frac{19.2086 \cdot 2500}{\sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}

Next Step Evaluate

∴

K = 0.800000000035223m

LAST Step Rounding Answer

∴

K = 0.8m

Maximum Displacement of Vibration given Transmissibility Ratio Formula Elements

Variables

Functions

Maximum Displacement

Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.

Symbol: K

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Maximum Displacement

Transmissibility Ratio

Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Transmissibility Ratio

Applied Force

Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.

Symbol: F_a

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Applied Force

Stiffness of Spring

Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.

Symbol: k

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Spring

Damping Coefficient

Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.

Symbol: c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value should be greater than 0.

Formulas to find Damping Coefficient

Angular Velocity

Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity

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 to find Maximum Displacement

Go Maximum Displacement of Vibration using Force Transmitted

K = \frac{F T}{\sqrt{k^{2} + {(c \cdot ω)}^{2}}}

Other formulas in Vibration Isolation and Transmissibility category

Go Angular Velocity of Vibration using Force Transmitted

ω = \frac{\sqrt{{(\frac{F T}{K})}^{2} - k^{2}}}{c}

Go Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

F a = \frac{K \cdot \sqrt{k^{2} + {(c \cdot ω)}^{2}}}{ε}

Go Applied Force given Transmissibility Ratio

F a = \frac{F T}{ε}

Go Damping Coefficient using Force Transmitted

c = \frac{\sqrt{{(\frac{F T}{K})}^{2} - k^{2}}}{ω}

How to Evaluate Maximum Displacement of Vibration given Transmissibility Ratio?

Maximum Displacement of Vibration given Transmissibility Ratio evaluator uses Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)) to evaluate the Maximum Displacement, Maximum Displacement of Vibration given Transmissibility Ratio formula is defined as a measure of the maximum amplitude of vibration of a system in terms of the transmissibility ratio, which is a critical parameter in mechanical vibration analysis, used to evaluate the vibration isolation effectiveness of a system. Maximum Displacement is denoted by K symbol.

How to evaluate Maximum Displacement of Vibration given Transmissibility Ratio using this online evaluator? To use this online evaluator for Maximum Displacement of Vibration given Transmissibility Ratio, enter Transmissibility Ratio (ε), Applied Force (F_a), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω) and hit the calculate button.

FAQs on Maximum Displacement of Vibration given Transmissibility Ratio

What is the formula to find Maximum Displacement of Vibration given Transmissibility Ratio?

The formula of Maximum Displacement of Vibration given Transmissibility Ratio is expressed as Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)). Here is an example- 0.8 = (19.20864*2500)/(sqrt(60000^2+(9000.022*0.200022)^2)).

How to calculate Maximum Displacement of Vibration given Transmissibility Ratio?

With Transmissibility Ratio (ε), Applied Force (F_a), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω) we can find Maximum Displacement of Vibration given Transmissibility Ratio using the formula - Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Maximum Displacement?

Here are the different ways to Calculate Maximum Displacement-

Maximum Displacement=Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))

Can the Maximum Displacement of Vibration given Transmissibility Ratio be negative?

No, the Maximum Displacement of Vibration given Transmissibility Ratio, measured in Length cannot be negative.

Which unit is used to measure Maximum Displacement of Vibration given Transmissibility Ratio?

Maximum Displacement of Vibration given Transmissibility Ratio is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Maximum Displacement of Vibration given Transmissibility Ratio can be measured.

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Maximum Displacement of Vibration given Transmissibility Ratio Formula

​GoMaximum Displacement of Vibration using Force Transmitted Formula

Maximum Displacement of Vibration given Transmissibility Ratio Example

Maximum Displacement of Vibration given Transmissibility Ratio Solution

Maximum Displacement of Vibration given Transmissibility Ratio Formula Elements

Other Formulas to find Maximum Displacement

Other formulas in Vibration Isolation and Transmissibility category

How to Evaluate Maximum Displacement of Vibration given Transmissibility Ratio?

FAQs on Maximum Displacement of Vibration given Transmissibility Ratio

Variable Name

GoMaximum Displacement of Vibration using Force Transmitted Formula