Magnification Factor at Resonance Calculator

✖Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.ⓘ Stiffness of Spring [k]			+10% -10%
✖Damping coefficient is a material property that indicates whether a material will bounce back or return energy to a system.ⓘ Damping coefficient [c]			+10% -10%
✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%

✖Magnification Factor is the value of deflection under the dynamic force divided by the deflection under the static type of force.ⓘ Magnification Factor at Resonance [D]

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Formula

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Magnification Factor at Resonance

Formula

`"D" = "k"/("c"*"ω"_{"n"})`

Example

`"0.000714"="0.75N/m"/("50Ns/m"*"21rad/s")`

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Download Longitudinal and Transverse Vibrations Formula PDF

Magnification Factor at Resonance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Magnification Factor = Stiffness of Spring/(Damping coefficient*Natural Circular Frequency)
D = k/(c*ω_n)
This formula uses 4 Variables

Variables Used

Magnification Factor - Magnification Factor is the value of deflection under the dynamic force divided by the deflection under the static type of force.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.
Damping coefficient - (Measured in Newton Second per Meter) - Damping coefficient is a material property that indicates whether a material will bounce back or return energy to a system.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.

STEP 1: Convert Input(s) to Base Unit

Stiffness of Spring: 0.75 Newton per Meter --> 0.75 Newton per Meter No Conversion Required
Damping coefficient: 50 Newton Second per Meter --> 50 Newton Second per Meter No Conversion Required
Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = k/(c*ω_n) --> 0.75/(50*21)

Evaluating ... ...

D = 0.000714285714285714

STEP 3: Convert Result to Output's Unit

0.000714285714285714 --> No Conversion Required

FINAL ANSWER

0.000714285714285714 ≈ 0.000714 <-- Magnification Factor

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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< 6 Magnification Factor or Dynamic Magnifier Calculators

Magnification Factor

Go Magnification Factor = 1/(sqrt((Damping coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2))

Magnification Factor if there is No Damping

Go Magnification Factor = (Natural Circular Frequency^2)/(Natural Circular Frequency^2-Angular Velocity^2)

Natural Circular Frequency given Magnification Factor

Go Natural Circular Frequency = Stiffness of Spring/(Magnification Factor*Damping coefficient)

Magnification Factor at Resonance

Go Magnification Factor = Stiffness of Spring/(Damping coefficient*Natural Circular Frequency)

Magnification Factor given Displacement of Vibrations

Go Magnification Factor = Total Displacement/Deflection under the static force

Maximum Displacement given Magnification Factor

Go Total Displacement = Magnification Factor*Deflection under the static force

Magnification Factor at Resonance Formula

Magnification Factor = Stiffness of Spring/(Damping coefficient*Natural Circular Frequency)
D = k/(c*ω_n)

What is dynamic magnification factor?

Dynamic magnification factor is defined as the ratio of the dynamic deflection at any time to the static deflection which would have resulted from the static application of the external load, which is used in specifying the load-time variation.

How to Calculate Magnification Factor at Resonance?

Magnification Factor at Resonance calculator uses Magnification Factor = Stiffness of Spring/(Damping coefficient*Natural Circular Frequency) to calculate the Magnification Factor, Magnification factor at resonance formula is defined as the the ratio of the spring stiffness to the product of the damping coefficient and the natural circular frequency. Magnification Factor is denoted by D symbol.

How to calculate Magnification Factor at Resonance using this online calculator? To use this online calculator for Magnification Factor at Resonance, enter Stiffness of Spring (k), Damping coefficient (c) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Magnification Factor at Resonance calculation can be explained with given input values -> 0.000714 = 0.75/(50*21).

FAQ

What is Magnification Factor at Resonance?

Magnification factor at resonance formula is defined as the the ratio of the spring stiffness to the product of the damping coefficient and the natural circular frequency and is represented as D = k/(c*ω_n) or Magnification Factor = Stiffness of Spring/(Damping coefficient*Natural Circular Frequency). Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness, Damping coefficient is a material property that indicates whether a material will bounce back or return energy to a system & Natural Circular Frequency is a scalar measure of rotation rate.

How to calculate Magnification Factor at Resonance?

Magnification factor at resonance formula is defined as the the ratio of the spring stiffness to the product of the damping coefficient and the natural circular frequency is calculated using Magnification Factor = Stiffness of Spring/(Damping coefficient*Natural Circular Frequency). To calculate Magnification Factor at Resonance, you need Stiffness of Spring (k), Damping coefficient (c) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Stiffness of Spring, Damping coefficient & Natural Circular Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Magnification Factor?

In this formula, Magnification Factor uses Stiffness of Spring, Damping coefficient & Natural Circular Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

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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