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Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Formula

GoMagnification Factor given Transmissibility Ratio 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}{\sqrt{1 + {(\frac{2 \cdot c \cdot ω}{c c \cdot ω n})}^{2}}}

D - Magnification Factor?ε - Transmissibility Ratio?c - Damping Coefficient?ω - Angular Velocity?c_c - Critical Damping Coefficient?ω_n - Natural Circular Frequency?

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Example

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

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

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

19.2018 = \frac{19.2086}{\sqrt{1 + {(\frac{2 \cdot 9000.022 \cdot 0.2}{690000 \cdot 0.195})}^{2}}}

19.2018 = \frac{19.2086}{\sqrt{1 + {(\frac{2 \cdot 9000.022Ns/m \cdot 0.2rad/s}{690000Ns/m \cdot 0.195rad/s})}^{2}}}

19.2018 = \frac{19.2086}{\sqrt{1 + {(\frac{2 \cdot 9000.022 \cdot 0.2}{690000 \cdot 0.195})}^{2}}}

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Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

D = \frac{19.2086}{\sqrt{1 + {(\frac{2 \cdot 9000.022Ns/m \cdot 0.2rad/s}{690000Ns/m \cdot 0.195rad/s})}^{2}}}

Next Step Prepare to Evaluate

∴

D = \frac{19.2086}{\sqrt{1 + {(\frac{2 \cdot 9000.022 \cdot 0.2}{690000 \cdot 0.195})}^{2}}}

Next Step Evaluate

∴

D = 19.2017673502413

LAST Step Rounding Answer

∴

D = 19.2018

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency 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

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

Critical Damping Coefficient

Critical Damping Coefficient is the minimum amount of damping required to prevent oscillations in a mechanical system, resulting in a critically damped response.

Symbol: c_c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value should be greater than 0.

Formulas to find Critical Damping Coefficient

Natural Circular Frequency

Natural Circular Frequency is the number of oscillations per unit time of a vibrating system in a circular motion.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular Frequency

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

D = \frac{ε \cdot k}{\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 Magnification Factor given Transmissibility Ratio given Natural Circular Frequency?

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency evaluator uses Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)) to evaluate the Magnification Factor, Magnification Factor given Transmissibility Ratio given Natural Circular Frequency formula is defined as a dimensionless quantity that expresses the ratio of the amplitude of the transmitted vibration to the amplitude of the incident vibration in a mechanical system, providing a measure of the reduction in vibration amplitude. Magnification Factor is denoted by D symbol.

How to evaluate Magnification Factor given Transmissibility Ratio given Natural Circular Frequency using this online evaluator? To use this online evaluator for Magnification Factor given Transmissibility Ratio given Natural Circular Frequency, enter Transmissibility Ratio (ε), Damping Coefficient (c), Angular Velocity (ω), Critical Damping Coefficient (c_c) & Natural Circular Frequency (ω_n) and hit the calculate button.

FAQs on Magnification Factor given Transmissibility Ratio given Natural Circular Frequency

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

The formula of Magnification Factor given Transmissibility Ratio given Natural Circular Frequency is expressed as Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)). Here is an example- 19.20196 = 19.20864/(sqrt(1+((2*9000.022*0.200022)/(690000*0.19501))^2)).

How to calculate Magnification Factor given Transmissibility Ratio given Natural Circular Frequency?

With Transmissibility Ratio (ε), Damping Coefficient (c), Angular Velocity (ω), Critical Damping Coefficient (c_c) & Natural Circular Frequency (ω_n) we can find Magnification Factor given Transmissibility Ratio given Natural Circular Frequency using the formula - Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^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*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))

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Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Formula

​GoMagnification Factor given Transmissibility Ratio Formula

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Example

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Solution

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Formula Elements

Other Formulas to find Magnification Factor

Other formulas in Vibration Isolation and Transmissibility category

How to Evaluate Magnification Factor given Transmissibility Ratio given Natural Circular Frequency?

FAQs on Magnification Factor given Transmissibility Ratio given Natural Circular Frequency

Variable Name

GoMagnification Factor given Transmissibility Ratio Formula