Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Calculator

✖Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.ⓘ Maximum Displacement [K]			+10% -10%
✖Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.ⓘ Stiffness of Spring [k]			+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%
✖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%

✖Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.ⓘ Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration [F_a]

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Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio
F_a = (K*sqrt(k^2+(c*ω)^2))/ε
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

Applied Force - (Measured in Newton) - Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.
Maximum Displacement - (Measured in Meter) - Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.
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.
Transmissibility Ratio - Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.

STEP 1: Convert Input(s) to Base Unit

Maximum Displacement: 0.8 Meter --> 0.8 Meter No Conversion Required
Stiffness of Spring: 60000 Newton per Meter --> 60000 Newton per Meter 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
Transmissibility Ratio: 19.20864 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_a = (K*sqrt(k^2+(c*ω)^2))/ε --> (0.8*sqrt(60000^2+(9000.022*0.200022)^2))/19.20864

Evaluating ... ...

F_a = 2499.99999988993

STEP 3: Convert Result to Output's Unit

2499.99999988993 Newton --> No Conversion Required

FINAL ANSWER

2499.99999988993 ≈ 2500 Newton <-- Applied Force

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Vibration Isolation and Transmissibility » Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 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

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Formula

LaTeX Go

Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio
F_a = (K*sqrt(k^2+(c*ω)^2))/ε

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 Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration?

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration calculator uses Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio to calculate the Applied Force, Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration formula is defined as a measure of the force applied to a system in mechanical vibrations, which is influenced by the transmissibility ratio and maximum displacement of vibration, and is a critical parameter in understanding the dynamic behavior of vibrating systems. Applied Force is denoted by F_a symbol.

How to calculate Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration using this online calculator? To use this online calculator for Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration, enter Maximum Displacement (K), Stiffness of Spring (k), Damping Coefficient (c), Angular Velocity (ω) & Transmissibility Ratio (ε) and hit the calculate button. Here is how the Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration calculation can be explained with given input values -> 2500 = (0.8*sqrt(60000^2+(9000.022*0.200022)^2))/19.20864.

FAQ

What is Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration?

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration formula is defined as a measure of the force applied to a system in mechanical vibrations, which is influenced by the transmissibility ratio and maximum displacement of vibration, and is a critical parameter in understanding the dynamic behavior of vibrating systems and is represented as F_a = (K*sqrt(k^2+(c*ω)^2))/ε or Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio. Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system, Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched, 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 & Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.

How to calculate Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration?

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration formula is defined as a measure of the force applied to a system in mechanical vibrations, which is influenced by the transmissibility ratio and maximum displacement of vibration, and is a critical parameter in understanding the dynamic behavior of vibrating systems is calculated using Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio. To calculate Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration, you need Maximum Displacement (K), Stiffness of Spring (k), Damping Coefficient (c), Angular Velocity (ω) & Transmissibility Ratio (ε). With our tool, you need to enter the respective value for Maximum Displacement, Stiffness of Spring, Damping Coefficient, Angular Velocity & Transmissibility Ratio 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 Applied Force?

In this formula, Applied Force uses Maximum Displacement, Stiffness of Spring, Damping Coefficient, Angular Velocity & Transmissibility Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -

Applied Force = Force Transmitted/Transmissibility Ratio
Applied Force = Force Transmitted/Transmissibility Ratio

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