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Transmissibility Ratio given Magnification Factor Formula

GoTransmissibility Ratio Formula

GoTransmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Formula

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

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

ε - Transmissibility Ratio?D - Magnification Factor?k - Stiffness of Spring?c - Damping Coefficient?ω - Angular Velocity?

Transmissibility Ratio given Magnification Factor Example

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Here is how the Transmissibility Ratio given Magnification Factor equation looks like with Values.

Here is how the Transmissibility Ratio given Magnification Factor equation looks like with Units.

Here is how the Transmissibility Ratio given Magnification Factor equation looks like.

19.2086 = \frac{19.2 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{60000}

19.2086 = \frac{19.2 \cdot \sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}{60000N/m}

19.2086 = \frac{19.2 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{60000}

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Transmissibility Ratio given Magnification Factor Solution

Follow our step by step solution on how to calculate Transmissibility Ratio given Magnification Factor?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ε = \frac{19.2 \cdot \sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}{60000N/m}

Next Step Prepare to Evaluate

∴

ε = \frac{19.2 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{60000}

Next Step Evaluate

∴

ε = 19.2086399991543

LAST Step Rounding Answer

∴

ε = 19.2086

Transmissibility Ratio given Magnification Factor Formula Elements

Variables

Functions

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

Magnification Factor

Magnification Factor is the ratio of the amplitude of the vibrating body to the amplitude of the force causing the vibration.

Symbol: D

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Magnification Factor

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 Transmissibility Ratio

Go Transmissibility Ratio

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

Go Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient

ε = \frac{\sqrt{1 + (\frac{2 \cdot c \cdot ω}{{(c c \cdot ω n)}^{2}})}}{\sqrt{{(\frac{2 \cdot c \cdot ω}{c c \cdot ω n})}^{2} + {(1 - {(\frac{ω}{ω n})}^{2})}^{2}}}

Go Transmissibility Ratio given Natural Circular Frequency and Magnification Factor

ε = D \cdot \sqrt{1 + {(\frac{2 \cdot c \cdot ω}{c c \cdot ω n})}^{2}}

Go Transmissibility Ratio if there is No Damping

ε = \frac{1}{{(\frac{ω}{ω n})}^{2} - 1}

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 Transmissibility Ratio given Magnification Factor?

Transmissibility Ratio given Magnification Factor evaluator uses Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring to evaluate the Transmissibility Ratio, Transmissibility Ratio given Magnification Factor formula is defined as a measure of the ratio of the amplitude of the force transmitted to the foundation to the amplitude of the force applied to the system, which is an essential parameter in mechanical vibrations to analyze the dynamic behavior of systems. Transmissibility Ratio is denoted by ε symbol.

How to evaluate Transmissibility Ratio given Magnification Factor using this online evaluator? To use this online evaluator for Transmissibility Ratio given Magnification Factor, enter Magnification Factor (D), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω) and hit the calculate button.

FAQs on Transmissibility Ratio given Magnification Factor

What is the formula to find Transmissibility Ratio given Magnification Factor?

The formula of Transmissibility Ratio given Magnification Factor is expressed as Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring. Here is an example- 19.19864 = (19.2*sqrt(60000^2+(9000.022*0.200022)^2))/60000.

How to calculate Transmissibility Ratio given Magnification Factor?

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

What are the other ways to Calculate Transmissibility Ratio?

Here are the different ways to Calculate Transmissibility Ratio-

Transmissibility Ratio=(Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
Transmissibility Ratio=(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)
Transmissibility Ratio=Magnification Factor*sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)

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: Value
: Unit

Transmissibility Ratio given Magnification Factor Formula

​GoTransmissibility Ratio Formula

​GoTransmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Formula

Transmissibility Ratio given Magnification Factor Example

Transmissibility Ratio given Magnification Factor Solution

Transmissibility Ratio given Magnification Factor Formula Elements

Other Formulas to find Transmissibility Ratio

Other formulas in Vibration Isolation and Transmissibility category

How to Evaluate Transmissibility Ratio given Magnification Factor?

FAQs on Transmissibility Ratio given Magnification Factor

Variable Name

GoTransmissibility Ratio Formula

GoTransmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient Formula