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Magnification Factor given Transmissibility Ratio Formula

GoMagnification Factor given Transmissibility Ratio given Natural Circular Frequency Formula

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

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

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

Magnification Factor given Transmissibility Ratio Example

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

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

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

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

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

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

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Magnification Factor given Transmissibility Ratio Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

D = 19.2000000008453

LAST Step Rounding Answer

∴

D = 19.2

Magnification Factor given Transmissibility Ratio Formula Elements

Variables

Functions

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

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

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 Magnification Factor

Go Magnification Factor given Transmissibility Ratio given Natural Circular Frequency

D = \frac{ε}{\sqrt{1 + {(\frac{2 \cdot c \cdot ω}{c c \cdot ω n})}^{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 Magnification Factor given Transmissibility Ratio?

Magnification Factor given Transmissibility Ratio evaluator uses Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)) to evaluate the Magnification Factor, Magnification Factor given Transmissibility Ratio formula is defined as a dimensionless quantity that expresses the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave in a mechanical vibration system, providing a measure of the energy transmission through the system. Magnification Factor is denoted by D symbol.

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

FAQs on Magnification Factor given Transmissibility Ratio

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

The formula of Magnification Factor given Transmissibility Ratio is expressed as Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)). Here is an example- 19.2 = (19.20864*60000)/(sqrt(60000^2+(9000.022*0.200022)^2)).

How to calculate Magnification Factor given Transmissibility Ratio?

With Transmissibility Ratio (ε), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω) we can find Magnification Factor given Transmissibility Ratio using the formula - Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(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 Magnification Factor?

Here are the different ways to Calculate Magnification Factor-

Magnification Factor=Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))

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: Unit

Magnification Factor given Transmissibility Ratio Formula

​GoMagnification Factor given Transmissibility Ratio given Natural Circular Frequency Formula

Magnification Factor given Transmissibility Ratio Example

Magnification Factor given Transmissibility Ratio Solution

Magnification Factor given Transmissibility Ratio Formula Elements

Other Formulas to find Magnification Factor

Other formulas in Vibration Isolation and Transmissibility category

How to Evaluate Magnification Factor given Transmissibility Ratio?

FAQs on Magnification Factor given Transmissibility Ratio

Variable Name

GoMagnification Factor given Transmissibility Ratio given Natural Circular Frequency Formula