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Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Formula

GoApplied Force given Transmissibility Ratio Formula

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Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations. Check FAQs

F a = \frac{K \cdot \sqrt{k^{2} + {(c \cdot ω)}^{2}}}{ε}

F_a - Applied Force?K - Maximum Displacement?k - Stiffness of Spring?c - Damping Coefficient?ω - Angular Velocity?ε - Transmissibility Ratio?

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Example

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Here is how the Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration equation looks like with Values.

Here is how the Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration equation looks like with Units.

Here is how the Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration equation looks like.

2500 = \frac{0.8 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{19.2086}

2500N = \frac{0.8m \cdot \sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}{19.2086}

2500 = \frac{0.8 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{19.2086}

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Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Solution

Follow our step by step solution on how to calculate Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration?

FIRST Step Consider the formula

F a = \frac{K \cdot \sqrt{k^{2} + {(c \cdot ω)}^{2}}}{ε}

Next Step Substitute values of Variables

∴

F a = \frac{0.8m \cdot \sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}{19.2086}

Next Step Prepare to Evaluate

∴

F a = \frac{0.8 \cdot \sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}{19.2086}

Next Step Evaluate

∴

F a = 2499.99999988993N

LAST Step Rounding Answer

∴

F a = 2500N

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Formula Elements

Variables

Functions

Applied Force

Applied Force is the force that is intentionally applied to a system to induce or maintain mechanical vibrations.

Symbol: F_a

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Applied Force

Maximum Displacement

Maximum Displacement is the greatest distance from the mean position that an oscillating object reaches in a mechanical vibrating system.

Symbol: K

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Maximum Displacement

Stiffness of Spring

Stiffness of Spring is the measure of a spring's resistance to deformation, indicating its ability to store energy when compressed or stretched.

Symbol: k

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Spring

Damping Coefficient

Damping Coefficient is a measure of the rate at which the amplitude of oscillations decreases in a mechanical system due to energy loss.

Symbol: c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value should be greater than 0.

Formulas to find Damping Coefficient

Angular Velocity

Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity

Transmissibility Ratio

Transmissibility Ratio is the ratio of the response amplitude of a system to the excitation amplitude in mechanical vibration analysis.

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Transmissibility Ratio

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.

Syntax: sqrt(Number)

Other Formulas to find Applied Force

Go Applied Force given Transmissibility Ratio

F a = \frac{F T}{ε}

Other formulas in Vibration Isolation and Transmissibility category

Go Angular Velocity of Vibration using Force Transmitted

ω = \frac{\sqrt{{(\frac{F T}{K})}^{2} - k^{2}}}{c}

Go Damping Coefficient using Force Transmitted

c = \frac{\sqrt{{(\frac{F T}{K})}^{2} - k^{2}}}{ω}

Go Force Transmitted

F T = K \cdot \sqrt{k^{2} + {(c \cdot ω)}^{2}}

Go Magnification Factor given Transmissibility Ratio

D = \frac{ε \cdot k}{\sqrt{k^{2} + {(c \cdot ω)}^{2}}}

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

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration evaluator uses Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio to evaluate 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 evaluate Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration using this online evaluator? To use this online evaluator 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.

FAQs on Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

What is the formula to find Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration?

The formula of Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration is expressed as Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio. Here is an example- 2500 = (0.8*sqrt(60000^2+(9000.022*0.200022)^2))/19.20864.

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

With Maximum Displacement (K), Stiffness of Spring (k), Damping Coefficient (c), Angular Velocity (ω) & Transmissibility Ratio (ε) we can find Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration using the formula - Applied Force = (Maximum Displacement*sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2))/Transmissibility Ratio. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Applied Force?

Here are the different ways to Calculate Applied Force-

Applied Force=Force Transmitted/Transmissibility Ratio

Can the Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration be negative?

No, the Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration, measured in Force cannot be negative.

Which unit is used to measure Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration?

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration can be measured.

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Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Formula

​GoApplied Force given Transmissibility Ratio Formula

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Example

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Solution

Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration Formula Elements

Other Formulas to find Applied Force

Other formulas in Vibration Isolation and Transmissibility category

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

FAQs on Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

Variable Name

GoApplied Force given Transmissibility Ratio Formula