✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+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%

✖Magnification Factor is the value of deflection under the dynamic force divided by the deflection under the static type of force.ⓘ Magnification Factor if there is No Damping [D]

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Formula

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Magnification Factor if there is No Damping

Formula

`"D" = ("ω"_{"n"}^2)/("ω"_{"n"}^2-"ω"^2)`

Example

`"1.397516"=(("21rad/s")^2)/(("21rad/s")^2-("11.2rad/s")^2)`

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Magnification Factor if there is No Damping Solution

STEP 0: Pre-Calculation Summary

Formula Used

Magnification Factor = (Natural Circular Frequency^2)/(Natural Circular Frequency^2-Angular Velocity^2)
D = (ω_n^2)/(ω_n^2-ω^2)
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.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
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.

STEP 1: Convert Input(s) to Base Unit

Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = (ω_n^2)/(ω_n^2-ω^2) --> (21^2)/(21^2-11.2^2)

Evaluating ... ...

D = 1.39751552795031

STEP 3: Convert Result to Output's Unit

1.39751552795031 --> No Conversion Required

FINAL ANSWER

1.39751552795031 ≈ 1.397516 <-- Magnification Factor

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Magnification Factor or Dynamic Magnifier » Magnification Factor if there is No Damping

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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 if there is No Damping Formula

Magnification Factor = (Natural Circular Frequency^2)/(Natural Circular Frequency^2-Angular Velocity^2)
D = (ω_n^2)/(ω_n^2-ω^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 if there is No Damping?

Magnification Factor if there is No Damping calculator uses Magnification Factor = (Natural Circular Frequency^2)/(Natural Circular Frequency^2-Angular Velocity^2) to calculate the Magnification Factor, The Magnification factor if there is no damping formula is defined as the square of the natural circular frequency and dividing it by the difference between the square of the natural circular frequency and the square of the angular velocity. Magnification Factor is denoted by D symbol.

How to calculate Magnification Factor if there is No Damping using this online calculator? To use this online calculator for Magnification Factor if there is No Damping, enter Natural Circular Frequency (ω_n) & Angular Velocity (ω) and hit the calculate button. Here is how the Magnification Factor if there is No Damping calculation can be explained with given input values -> 1.397516 = (21^2)/(21^2-11.2^2).

FAQ

What is Magnification Factor if there is No Damping?

The Magnification factor if there is no damping formula is defined as the square of the natural circular frequency and dividing it by the difference between the square of the natural circular frequency and the square of the angular velocity and is represented as D = (ω_n^2)/(ω_n^2-ω^2) or Magnification Factor = (Natural Circular Frequency^2)/(Natural Circular Frequency^2-Angular Velocity^2). Natural Circular Frequency is a scalar measure of rotation rate & 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.

How to calculate Magnification Factor if there is No Damping?

The Magnification factor if there is no damping formula is defined as the square of the natural circular frequency and dividing it by the difference between the square of the natural circular frequency and the square of the angular velocity is calculated using Magnification Factor = (Natural Circular Frequency^2)/(Natural Circular Frequency^2-Angular Velocity^2). To calculate Magnification Factor if there is No Damping, you need Natural Circular Frequency (ω_n) & Angular Velocity (ω). With our tool, you need to enter the respective value for Natural Circular Frequency & Angular Velocity 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 Natural Circular Frequency & Angular Velocity. 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 = 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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