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)/(cc*ωn))^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 value of deflection under the dynamic force divided by the deflection under the static type of force.
Transmissibility Ratio - Transmissibility Ratio is the ratio of the force transmitted (FT) to the force applied (F) is known as the isolation factor or transmissibility ratio of the spring support.
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.
Critical Damping Coefficient - (Measured in Newton Second per Meter) - Critical damping coefficient provides the quickest approach to zero amplitude for a damped oscillator.
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
Transmissibility Ratio: 19.2 --> No Conversion Required
Damping Coefficient: 9000 Newton Second per Meter --> 9000 Newton Second per Meter No Conversion Required
Angular Velocity: 0.2 Radian per Second --> 0.2 Radian per Second No Conversion Required
Critical Damping Coefficient: 1800 Newton Second per Meter --> 1800 Newton Second per Meter No Conversion Required
Natural Circular Frequency: 0.194 Radian per Second --> 0.194 Radian per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
D = ε/(sqrt(1+((2*c*ω)/(ccn))^2)) --> 19.2/(sqrt(1+((2*9000*0.2)/(1800*0.194))^2))
Evaluating ... ...
D = 1.85369968721785
STEP 3: Convert Result to Output's Unit
1.85369968721785 --> No Conversion Required
FINAL ANSWER
1.85369968721785 1.8537 <-- Magnification Factor
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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18 Vibration Isolation and Transmissibility Calculators

Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient
Go Transmissibility Ratio = (sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)
Magnification Factor given Transmissibility Ratio given Natural Circular Frequency
Go Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))
Transmissibility Ratio given Natural Circular Frequency and Magnification Factor
Go Transmissibility Ratio = Magnification Factor*sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)
Magnification Factor given Transmissibility Ratio
Go Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Transmissibility Ratio given Magnification Factor
Go Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring
Maximum Displacement of Vibration given Transmissibility Ratio
Go Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration
Go Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio
Transmissibility Ratio
Go Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
Maximum Displacement of Vibration using Force Transmitted
Go Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Angular Velocity of Vibration using Force Transmitted
Go Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient
Stiffness of Spring using Force Transmitted
Go Stiffness of Spring = sqrt((Force Transmitted/Maximum Displacement)^2-(Damping Coefficient*Angular Velocity)^2)
Damping Coefficient using Force Transmitted
Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity
Force Transmitted
Go Force Transmitted = Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)
Natural Circular Frequency given Transmissibility Ratio
Go Natural Circular Frequency = Angular Velocity/(sqrt(1+1/Transmissibility Ratio))
Transmissibility Ratio if there is No Damping
Go Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1)
Transmissibility Ratio given Force Transmitted
Go Transmissibility Ratio = Force Transmitted/Applied Force
Transmitted Force given Transmissibility Ratio
Go Force Transmitted = Transmissibility Ratio*Applied Force
Applied Force given Transmissibility Ratio
Go Applied Force = Force Transmitted/Transmissibility Ratio

18 Forced Vibration Calculators

Transmissibility Ratio given Natural Circular Frequency and Critical Damping Coefficient
Go Transmissibility Ratio = (sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency)^2)))/sqrt(((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2)
Magnification Factor given Transmissibility Ratio given Natural Circular Frequency
Go Magnification Factor = Transmissibility Ratio/(sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2))
Transmissibility Ratio given Natural Circular Frequency and Magnification Factor
Go Transmissibility Ratio = Magnification Factor*sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)
Magnification Factor given Transmissibility Ratio
Go Magnification Factor = (Transmissibility Ratio*Stiffness of Spring)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Transmissibility Ratio given Magnification Factor
Go Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring
Maximum Displacement of Vibration given Transmissibility Ratio
Go Maximum Displacement = (Transmissibility Ratio*Applied Force)/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration
Go Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio
Transmissibility Ratio
Go Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
Maximum Displacement of Vibration using Force Transmitted
Go Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))
Angular Velocity of Vibration using Force Transmitted
Go Angular Velocity = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Damping Coefficient
Damping Coefficient using Force Transmitted
Go Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity
Stiffness of Spring using Force Transmitted
Go Stiffness of Spring = sqrt((Force Transmitted/Maximum Displacement)^2-(Damping Coefficient*Angular Velocity)^2)
Force Transmitted
Go Force Transmitted = Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)
Natural Circular Frequency given Transmissibility Ratio
Go Natural Circular Frequency = Angular Velocity/(sqrt(1+1/Transmissibility Ratio))
Transmissibility Ratio if there is No Damping
Go Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1)
Transmissibility Ratio given Force Transmitted
Go Transmissibility Ratio = Force Transmitted/Applied Force
Transmitted Force given Transmissibility Ratio
Go Force Transmitted = Transmissibility Ratio*Applied Force
Applied Force given Transmissibility Ratio
Go Applied Force = Force Transmitted/Transmissibility Ratio

Magnification Factor given Transmissibility Ratio given Natural Circular Frequency Formula

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)/(cc*ωn))^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, The Magnification factor given transmissibility ratio given natural circular frequency formula 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. 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 (cc) & Natural Circular Frequency 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 -> 18.82277 = 19.2/(sqrt(1+((2*9000*0.2)/(1800*0.194))^2)).

FAQ

What is Magnification Factor given Transmissibility Ratio given Natural Circular Frequency?
The Magnification factor given transmissibility ratio given natural circular frequency formula 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 and is represented as D = ε/(sqrt(1+((2*c*ω)/(ccn))^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 force transmitted (FT) to the force applied (F) is known as the isolation factor or transmissibility ratio of the spring support, 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, Critical damping coefficient provides the quickest approach to zero amplitude for a damped oscillator & Natural Circular Frequency is a scalar measure of rotation rate.
How to calculate Magnification Factor given Transmissibility Ratio given Natural Circular Frequency?
The Magnification factor given transmissibility ratio given natural circular frequency formula 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 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 (cc) & Natural Circular Frequency 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))
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