Magnification Factor given Displacement of Vibrations Calculator

✖Total Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.ⓘ Total Displacement [d_mass]			+10% -10%
✖Deflection under the static force is the deflection of system caused due to static force.ⓘ Deflection under the static force [x_o]			+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 given Displacement of Vibrations [D]

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Magnification Factor given Displacement of Vibrations

Formula

`"D" = "d"_{"mass"}/"x"_{"o"}`

Example

`"7.7"="15.4mm"/"2mm"`

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Download Longitudinal and Transverse Vibrations Formula PDF

Magnification Factor given Displacement of Vibrations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Magnification Factor = Total Displacement/Deflection under the static force
D = d_mass/x_o
This formula uses 3 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.
Total Displacement - (Measured in Meter) - Total Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
Deflection under the static force - (Measured in Meter) - Deflection under the static force is the deflection of system caused due to static force.

STEP 1: Convert Input(s) to Base Unit

Total Displacement: 15.4 Millimeter --> 0.0154 Meter (Check conversion here)
Deflection under the static force: 2 Millimeter --> 0.002 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = d_mass/x_o --> 0.0154/0.002

Evaluating ... ...

D = 7.7

STEP 3: Convert Result to Output's Unit

7.7 --> No Conversion Required

FINAL ANSWER

7.7 <-- Magnification Factor

(Calculation completed in 00.004 seconds)

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

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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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 given Displacement of Vibrations Formula

Magnification Factor = Total Displacement/Deflection under the static force
D = d_mass/x_o

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 given Displacement of Vibrations?

Magnification Factor given Displacement of Vibrations calculator uses Magnification Factor = Total Displacement/Deflection under the static force to calculate the Magnification Factor, The Magnification Factor given Displacement of Vibrations formula is defined as the value of deflection under the dynamic force divided by the deflection under the static type of force. Magnification Factor is denoted by D symbol.

How to calculate Magnification Factor given Displacement of Vibrations using this online calculator? To use this online calculator for Magnification Factor given Displacement of Vibrations, enter Total Displacement (d_mass) & Deflection under the static force (x_o) and hit the calculate button. Here is how the Magnification Factor given Displacement of Vibrations calculation can be explained with given input values -> 7.7 = 0.0154/0.002.

FAQ

What is Magnification Factor given Displacement of Vibrations?

The Magnification Factor given Displacement of Vibrations formula is defined as the value of deflection under the dynamic force divided by the deflection under the static type of force and is represented as D = d_mass/x_o or Magnification Factor = Total Displacement/Deflection under the static force. Total Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position & Deflection under the static force is the deflection of system caused due to static force.

How to calculate Magnification Factor given Displacement of Vibrations?

The Magnification Factor given Displacement of Vibrations formula is defined as the value of deflection under the dynamic force divided by the deflection under the static type of force is calculated using Magnification Factor = Total Displacement/Deflection under the static force. To calculate Magnification Factor given Displacement of Vibrations, you need Total Displacement (d_mass) & Deflection under the static force (x_o). With our tool, you need to enter the respective value for Total Displacement & Deflection under the static force 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 Total Displacement & Deflection under the static force. 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 = 1/(sqrt((Damping coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2))

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