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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 force transmitted (FT) to the force applied (F) is known as the isolation factor or transmissibility ratio of the spring support. 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.

19.1986 = \frac{19.19 \cdot \sqrt{60000^{2} + {(9000 \cdot 0.2)}^{2}}}{60000}

19.1986 = \frac{19.19 \cdot \sqrt{{60000N/m}^{2} + {(9000Ns/m \cdot 0.2rad/s)}^{2}}}{60000N/m}

19.1986 = \frac{19.19 \cdot \sqrt{60000^{2} + {(9000 \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{19.19 \cdot \sqrt{{60000N/m}^{2} + {(9000Ns/m \cdot 0.2rad/s)}^{2}}}{60000N/m}

Next Step Prepare to Evaluate

∴

ε = \frac{19.19 \cdot \sqrt{60000^{2} + {(9000 \cdot 0.2)}^{2}}}{60000}

Next Step Evaluate

∴

ε = 19.1986335578864

LAST Step Rounding Answer

∴

ε = 19.1986

Transmissibility Ratio given Magnification Factor Formula Elements

Variables

Functions

Transmissibility Ratio

Transmissibility Ratio is the ratio of the force transmitted (FT) to the force applied (F) is known as the isolation factor or transmissibility ratio of the spring support.

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Transmissibility Ratio

Magnification Factor

Magnification Factor is the value of deflection under the dynamic force divided by the deflection under the static type of force.

Symbol: D

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Magnification Factor

Stiffness of Spring

Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.

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 material property that indicates whether a material will bounce back or return energy to a system.

Symbol: c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value should be greater than 0.

Formulas to find Damping Coefficient

Angular Velocity

The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.

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, The Transmissibility Ratio given Magnification Factor formula is defined as the ratio of the force transmitted (FT) to the force applied (F) is known as the isolation factor or transmissibility ratio of the spring support. 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- 19.19 = (19.19*sqrt(60000^2+(9000*0.2)^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 Function 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