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Magnification Factor Formula

GoMagnification Factor at Resonance Formula

GoMagnification Factor if there is No Damping Formula

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

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

D - Magnification Factor?c - Damping Coefficient?ω - Angular Velocity?k - Stiffness of Spring?ω_n - Natural Circular Frequency?

Magnification Factor Example

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With units

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

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

Here is how the Magnification Factor equation looks like.

0.0013 = \frac{1}{\sqrt{{(50 \cdot \frac{11.2}{0.75})}^{2} + {(1 - {(\frac{11.2}{15})}^{2})}^{2}}}

0.0013 = \frac{1}{\sqrt{{(50Ns/m \cdot \frac{11.2rad/s}{0.75N/m})}^{2} + {(1 - {(\frac{11.2rad/s}{15rad/s})}^{2})}^{2}}}

0.0013 = \frac{1}{\sqrt{{(50 \cdot \frac{11.2}{0.75})}^{2} + {(1 - {(\frac{11.2}{15})}^{2})}^{2}}}

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Magnification Factor Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

D = \frac{1}{\sqrt{{(50Ns/m \cdot \frac{11.2rad/s}{0.75N/m})}^{2} + {(1 - {(\frac{11.2rad/s}{15rad/s})}^{2})}^{2}}}

Next Step Prepare to Evaluate

∴

D = \frac{1}{\sqrt{{(50 \cdot \frac{11.2}{0.75})}^{2} + {(1 - {(\frac{11.2}{15})}^{2})}^{2}}}

Next Step Evaluate

∴

D = 0.00133928547910899

LAST Step Rounding Answer

∴

D = 0.0013

Magnification Factor Formula Elements

Variables

Functions

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

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 should be greater than 0.

Formulas to find Angular Velocity

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

Natural Circular Frequency

Natural Circular Frequency is a scalar measure of rotation rate.

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 at Resonance

D = \frac{k}{c \cdot ω n}

Go Magnification Factor if there is No Damping

D = \frac{{ω n}^{2}}{{ω n}^{2} - ω^{2}}

Go Magnification Factor given Displacement of Vibrations

D = \frac{d mass}{x o}

Other formulas in Magnification Factor or Dynamic Magnifier category

Go Maximum Displacement given Magnification Factor

d mass = D \cdot x o

Go Natural Circular Frequency given Magnification Factor

ω n = \frac{k}{D \cdot c}

How to Evaluate Magnification Factor?

Magnification Factor evaluator uses Magnification Factor = 1/(sqrt((Damping Coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)) to evaluate the Magnification Factor, Magnification Factor formula is defined as a measure of the amplification of a system's response to an input, specifically in mechanical systems, where it quantifies the ratio of the output amplitude to the input amplitude, providing insight into the system's dynamic behavior and stability. Magnification Factor is denoted by D symbol.

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

FAQs on Magnification Factor

What is the formula to find Magnification Factor?

The formula of Magnification Factor is expressed as Magnification Factor = 1/(sqrt((Damping Coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)). Here is an example- 0.001339 = 1/(sqrt((50*11.2/0.75)^2+(1-(11.2/15)^2)^2)).

How to calculate Magnification Factor?

With Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Natural Circular Frequency (ω_n) we can find Magnification Factor using the formula - Magnification Factor = 1/(sqrt((Damping Coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^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=Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
Magnification Factor=(Natural Circular Frequency^2)/(Natural Circular Frequency^2-Angular Velocity^2)
Magnification Factor=Total Displacement/Deflection Under the Static Force

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: Value
: Unit

Magnification Factor Formula

​GoMagnification Factor at Resonance Formula

​GoMagnification Factor if there is No Damping Formula

Magnification Factor Example

Magnification Factor Solution

Magnification Factor Formula Elements

Other Formulas to find Magnification Factor

Other formulas in Magnification Factor or Dynamic Magnifier category

How to Evaluate Magnification Factor?

FAQs on Magnification Factor

Variable Name

GoMagnification Factor at Resonance Formula

GoMagnification Factor if there is No Damping Formula