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Magnification Factor at Resonance Formula

GoMagnification Factor if there is No Damping Formula

GoMagnification Factor 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{k}{c \cdot ω n}

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

Magnification Factor at Resonance Example

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

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

Here is how the Magnification Factor at Resonance equation looks like.

0.001 = \frac{0.75}{50 \cdot 15}

0.001 = \frac{0.75N/m}{50Ns/m \cdot 15rad/s}

0.001 = \frac{0.75}{50 \cdot 15}

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Magnification Factor at Resonance Solution

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

FIRST Step Consider the formula

D = \frac{k}{c \cdot ω n}

Next Step Substitute values of Variables

∴

D = \frac{0.75N/m}{50Ns/m \cdot 15rad/s}

Next Step Prepare to Evaluate

∴

D = \frac{0.75}{50 \cdot 15}

LAST Step Evaluate

∴

D = 0.001

Magnification Factor at Resonance Formula Elements

Variables

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

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

Other Formulas to find Magnification Factor

Go Magnification Factor if there is No Damping

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

Go Magnification Factor

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

Magnification Factor at Resonance evaluator uses Magnification Factor = Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency) to evaluate the Magnification Factor, Magnification Factor at Resonance formula is defined as a measure of the amplification of a vibrating system's oscillations when the frequency of the external force matches the natural frequency of the system, resulting in maximum energy transfer and increased amplitude of motion. Magnification Factor is denoted by D symbol.

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

FAQs on Magnification Factor at Resonance

What is the formula to find Magnification Factor at Resonance?

The formula of Magnification Factor at Resonance is expressed as Magnification Factor = Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency). Here is an example- 0.000714 = 0.75/(50*15).

How to calculate Magnification Factor at Resonance?

With Stiffness of Spring (k), Damping Coefficient (c) & Natural Circular Frequency (ω_n) we can find Magnification Factor at Resonance using the formula - Magnification Factor = Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency).

What are the other ways to Calculate Magnification Factor?

Here are the different ways to Calculate Magnification Factor-

Magnification Factor=(Natural Circular Frequency^2)/(Natural Circular Frequency^2-Angular Velocity^2)
Magnification Factor=1/(sqrt((Damping Coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2))
Magnification Factor=Total Displacement/Deflection Under the Static Force

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Magnification Factor at Resonance Formula

​GoMagnification Factor if there is No Damping Formula

​GoMagnification Factor Formula

Magnification Factor at Resonance Example

Magnification Factor at Resonance Solution

Magnification Factor at Resonance Formula Elements

Other Formulas to find Magnification Factor

Other formulas in Magnification Factor or Dynamic Magnifier category

How to Evaluate Magnification Factor at Resonance?

FAQs on Magnification Factor at Resonance

Variable Name

GoMagnification Factor if there is No Damping Formula

GoMagnification Factor Formula