Transmissibility Ratio if there is No Damping Calculator

✖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%
✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%

✖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.ⓘ Transmissibility Ratio if there is No Damping [ε]

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Formula

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Transmissibility Ratio if there is No Damping

Formula

`"ε" = 1/(("ω"/"ω"_{"n"})^2-1)`

Example

`"15.92047"=1/(("0.2rad/s"/"0.194rad/s")^2-1)`

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Transmissibility Ratio if there is No Damping Solution

STEP 0: Pre-Calculation Summary

Formula Used

Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1)
ε = 1/((ω/ω_n)^2-1)
This formula uses 3 Variables

Variables Used

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.
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.
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

Angular Velocity: 0.2 Radian per Second --> 0.2 Radian per Second 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

ε = 1/((ω/ω_n)^2-1) --> 1/((0.2/0.194)^2-1)

Evaluating ... ...

ε = 15.9204737732656

STEP 3: Convert Result to Output's Unit

15.9204737732656 --> No Conversion Required

FINAL ANSWER

15.9204737732656 ≈ 15.92047 <-- Transmissibility Ratio

(Calculation completed in 00.006 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Vibration Isolation and Transmissibility » Transmissibility Ratio if there is No Damping

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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

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

Transmissibility Ratio if there is No Damping Formula

Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1)
ε = 1/((ω/ω_n)^2-1)

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 Transmissibility Ratio if there is No Damping?

Transmissibility Ratio if there is No Damping calculator uses Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1) to calculate the Transmissibility Ratio, The Transmissibility ratio if there is no damping formula is defined as 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. Transmissibility Ratio is denoted by ε symbol.

How to calculate Transmissibility Ratio if there is No Damping using this online calculator? To use this online calculator for Transmissibility Ratio if there is No Damping, enter Angular Velocity (ω) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Transmissibility Ratio if there is No Damping calculation can be explained with given input values -> -1.000405 = 1/((0.2/0.194)^2-1).

FAQ

What is Transmissibility Ratio if there is No Damping?

The Transmissibility ratio if there is no damping formula is defined as 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 and is represented as ε = 1/((ω/ω_n)^2-1) or Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1). 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 & Natural Circular Frequency is a scalar measure of rotation rate.

How to calculate Transmissibility Ratio if there is No Damping?

The Transmissibility ratio if there is no damping formula is defined as 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 is calculated using Transmissibility Ratio = 1/((Angular Velocity/Natural Circular Frequency)^2-1). To calculate Transmissibility Ratio if there is No Damping, you need Angular Velocity (ω) & Natural Circular Frequency (ω_n). With our tool, you need to enter the respective value for Angular Velocity & 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 Transmissibility Ratio?

In this formula, Transmissibility Ratio uses Angular Velocity & Natural Circular Frequency. We can use 10 other way(s) to calculate the same, which is/are as follows -

Transmissibility Ratio = Force Transmitted/Applied Force
Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring
Transmissibility Ratio = Magnification Factor*sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)
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)
Transmissibility Ratio = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Applied Force
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)
Transmissibility Ratio = Magnification Factor*sqrt(1+((2*Damping Coefficient*Angular Velocity)/(Critical Damping Coefficient*Natural Circular Frequency))^2)
Transmissibility Ratio = (Magnification Factor*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Stiffness of Spring
Transmissibility Ratio = Force Transmitted/Applied Force

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