Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Calculator

✖Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.ⓘ Transmissibility Ratio [ε]			+10% -10%
✖Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.ⓘ Damping Coefficient [c]			+10% -10%
✖Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.ⓘ Angular Velocity [ω]			+10% -10%
✖Critical Damping Coefficient is the minimum amount of damping required to prevent oscillations in a mechanical system, resulting in a critically damped response.ⓘ Critical Damping Coefficient [c_c]			+10% -10%
✖Natural Circular Frequency is the number of oscillations per unit time of a vibrating system in a circular motion.ⓘ Natural Circular Frequency [ω_n]			+10% -10%

✖Magnification Factor is the ratio of the amplitude of the vibrating body to the amplitude of the force causing the vibration.ⓘ Magnification Factor given Transmissibility Ratio given Natural Circular Frequency [D]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Vibration Isolation and Transmissibility Formulas PDF PDF Image

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))
D = ε/(sqrt(1+((2*c*ω)/(c_c*ω_n))^2))
This formula uses 1 Functions, 6 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 ratio of the amplitude of the vibrating body to the amplitude of the force causing the vibration.
Transmissibility Ratio - Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.
Angular Velocity - (Measured in Radian per Second) - Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.
Critical Damping Coefficient - (Measured in Newton Second per Meter) - Critical Damping Coefficient is the minimum amount of damping required to prevent oscillations in a mechanical system, resulting in a critically damped response.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the number of oscillations per unit time of a vibrating system in a circular motion.

STEP 1: Convert Input(s) to Base Unit

Transmissibility Ratio: 19.20864 --> No Conversion Required
Damping Coefficient: 9000.022 Newton Second per Meter --> 9000.022 Newton Second per Meter No Conversion Required
Angular Velocity: 0.200022 Radian per Second --> 0.200022 Radian per Second No Conversion Required
Critical Damping Coefficient: 690000 Newton Second per Meter --> 690000 Newton Second per Meter No Conversion Required
Natural Circular Frequency: 0.19501 Radian per Second --> 0.19501 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

D = ε/(sqrt(1+((2*c*ω)/(c_c*ω_n))^2)) --> 19.20864/(sqrt(1+((2*9000.022*0.200022)/(690000*0.19501))^2))

Evaluating ... ...

D = 19.2017673502413

STEP 3: Convert Result to Output's Unit

19.2017673502413 --> No Conversion Required

FINAL ANSWER

19.2017673502413 ≈ 19.20177 <-- Magnification Factor

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Vibration Isolation and Transmissibility » Magnification Factor given Transmissibility Ratio given Natural Circular Frequency

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has verified this Calculator and 400+ more calculators!

< Vibration Isolation and Transmissibility Calculators

Maximum Displacement of Vibration using Force Transmitted

LaTeX Go Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))

Stiffness of Spring using Force Transmitted

LaTeX Go Stiffness of Spring = sqrt((Force Transmitted/Maximum Displacement)^2-(Damping Coefficient*Angular Velocity)^2)

Damping Coefficient using Force Transmitted

LaTeX Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity

Force Transmitted

LaTeX Go Force Transmitted = Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)

< Forced Vibration Calculators

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

LaTeX Go Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio

Angular Velocity of Vibration using Force Transmitted

LaTeX Go Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient

Damping Coefficient using Force Transmitted

LaTeX Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity

Applied Force given Transmissibility Ratio

LaTeX Go Applied Force = Force Transmitted/Transmissibility Ratio

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Formula

LaTeX Go

Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))
D = ε/(sqrt(1+((2*c*ω)/(c_c*ω_n))^2))

What is meant by Vibration Isolation?

Vibration isolation is a commonly used technique for reducing or suppressing unwanted vibrations in structures and machines. With this technique, the device or system of interest is isolated from the source of vibration through insertion of a resilient member or isolator.

How to Calculate Magnification Factor given Transmissibility Ratio given Natural Circular Frequency?

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency calculator uses Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)) to calculate the Magnification Factor, Magnification Factor given Transmissibility Ratio given Natural Circular Frequency formula is defined as a dimensionless quantity that expresses the ratio of the amplitude of the transmitted vibration to the amplitude of the incident vibration in a mechanical system, providing a measure of the reduction in vibration amplitude. Magnification Factor is denoted by D symbol.

How to calculate Magnification Factor given Transmissibility Ratio given Natural Circular Frequency using this online calculator? To use this online calculator for Magnification Factor given Transmissibility Ratio given Natural Circular Frequency, enter Transmissibility Ratio (ε), Damping Coefficient (c), Angular Velocity (ω), Critical Damping Coefficient (c_c) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Magnification Factor given Transmissibility Ratio given Natural Circular Frequency calculation can be explained with given input values -> 19.20196 = 19.20864/(sqrt(1+((2*9000.022*0.200022)/(690000*0.19501))^2)).

FAQ

What is Magnification Factor given Transmissibility Ratio given Natural Circular Frequency?

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency formula is defined as a dimensionless quantity that expresses the ratio of the amplitude of the transmitted vibration to the amplitude of the incident vibration in a mechanical system, providing a measure of the reduction in vibration amplitude and is represented as D = ε/(sqrt(1+((2*c*ω)/(c_c*ω_n))^2)) or Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)). Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis, Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss, Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations, Critical Damping Coefficient is the minimum amount of damping required to prevent oscillations in a mechanical system, resulting in a critically damped response & Natural Circular Frequency is the number of oscillations per unit time of a vibrating system in a circular motion.

How to calculate Magnification Factor given Transmissibility Ratio given Natural Circular Frequency?

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency formula is defined as a dimensionless quantity that expresses the ratio of the amplitude of the transmitted vibration to the amplitude of the incident vibration in a mechanical system, providing a measure of the reduction in vibration amplitude is calculated using Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)). To calculate Magnification Factor given Transmissibility Ratio given Natural Circular Frequency, you need Transmissibility Ratio (ε), Damping Coefficient (c), Angular Velocity (ω), Critical Damping Coefficient (c_c) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Transmissibility Ratio, Damping Coefficient, Angular Velocity, Critical 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 Transmissibility Ratio, Damping Coefficient, Angular Velocity, Critical Damping Coefficient & Natural Circular Frequency. We can use 2 other way(s) to calculate the same, which is/are as follows -

Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))

Home

FREE PDFs

🔍 Search