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
Fa = (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
Fa = (K*sqrt(k^2+(c*ω)^2))/ε --> (0.8*sqrt(60000^2+(9000.022*0.200022)^2))/19.20864
Evaluating ... ...
Fa = 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 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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Indian Institute of Information Technology (IIIT), Guwahati
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Vibration Isolation and Transmissibility Calculators

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

Forced Vibration Calculators

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
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
Applied Force given Transmissibility Ratio
​ Go Applied Force = Force Transmitted/Transmissibility Ratio

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Formula

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