Magnification Factor Calculator

✖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%
✖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.ⓘ Angular Velocity [ω]			+10% -10%
✖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%
✖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 [D]

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Formula

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Magnification Factor

Formula

`"D" = 1/(sqrt(("c"*"ω"/"k")^2+(1-("ω"/"ω"_{"n"})^2)^2))`

Example

`"0.001339"=1/(sqrt(("50Ns/m"*"11.2rad/s"/"0.75N/m")^2+(1-("11.2rad/s"/"21rad/s")^2)^2))`

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Download Longitudinal and Transverse Vibrations Formula PDF

Magnification Factor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Magnification Factor = 1/(sqrt((Damping coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2))
D = 1/(sqrt((c*ω/k)^2+(1-(ω/ω_n)^2)^2))
This formula uses 1 Functions, 5 Variables

Functions Used

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., sqrt(Number)

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.
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.
Angular Velocity - (Measured in Radian per Second) - 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.
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.
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

Damping coefficient: 50 Newton Second per Meter --> 50 Newton Second per Meter No Conversion Required
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Stiffness of Spring: 0.75 Newton per Meter --> 0.75 Newton 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 = 1/(sqrt((c*ω/k)^2+(1-(ω/ω_n)^2)^2)) --> 1/(sqrt((50*11.2/0.75)^2+(1-(11.2/21)^2)^2))

Evaluating ... ...

D = 0.00133928509928428

STEP 3: Convert Result to Output's Unit

0.00133928509928428 --> No Conversion Required

FINAL ANSWER

0.00133928509928428 ≈ 0.001339 <-- Magnification Factor

(Calculation completed in 00.007 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Magnification Factor or Dynamic Magnifier » Magnification Factor

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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 Formula

Magnification Factor = 1/(sqrt((Damping coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2))
D = 1/(sqrt((c*ω/k)^2+(1-(ω/ω_n)^2)^2))

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?

Magnification Factor calculator uses Magnification Factor = 1/(sqrt((Damping coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)) to calculate the Magnification Factor, The Magnification factor formula is found by combining damping, angular velocity, spring stiffness, and natural frequency to evaluate the effect of these factors on oscillation amplitudes. Magnification Factor is denoted by D symbol.

How to calculate Magnification Factor using this online calculator? To use this online calculator for Magnification Factor, enter Damping coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Magnification Factor calculation can be explained with given input values -> 0.001339 = 1/(sqrt((50*11.2/0.75)^2+(1-(11.2/21)^2)^2)).

FAQ

What is Magnification Factor?

The Magnification factor formula is found by combining damping, angular velocity, spring stiffness, and natural frequency to evaluate the effect of these factors on oscillation amplitudes and is represented as D = 1/(sqrt((c*ω/k)^2+(1-(ω/ω_n)^2)^2)) or Magnification Factor = 1/(sqrt((Damping coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)). Damping coefficient is a material property that indicates whether a material will bounce back or return energy to a system, 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, Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness & Natural Circular Frequency is a scalar measure of rotation rate.

How to calculate Magnification Factor?

The Magnification factor formula is found by combining damping, angular velocity, spring stiffness, and natural frequency to evaluate the effect of these factors on oscillation amplitudes is calculated using Magnification Factor = 1/(sqrt((Damping coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)). To calculate Magnification Factor, you need Damping coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Damping coefficient, Angular Velocity, Stiffness of Spring & 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 Damping coefficient, Angular Velocity, Stiffness of Spring & Natural Circular Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

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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