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Maximum Displacement of Vibration using Force Transmitted Formula

GoMaximum Displacement of Vibration given Transmissibility Ratio Formula

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

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

K - Maximum Displacement?F_T - Force Transmitted?k - Stiffness of Spring?c - Damping Coefficient?ω - Angular Velocity?

Maximum Displacement of Vibration using Force Transmitted Example

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Here is how the Maximum Displacement of Vibration using Force Transmitted equation looks like with Values.

Here is how the Maximum Displacement of Vibration using Force Transmitted equation looks like with Units.

Here is how the Maximum Displacement of Vibration using Force Transmitted equation looks like.

0.8 = \frac{48021.6}{\sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}

0.8m = \frac{48021.6N}{\sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}

0.8 = \frac{48021.6}{\sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}

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Maximum Displacement of Vibration using Force Transmitted Solution

Follow our step by step solution on how to calculate Maximum Displacement of Vibration using Force Transmitted?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

K = \frac{48021.6N}{\sqrt{{60000N/m}^{2} + {(9000.022Ns/m \cdot 0.2rad/s)}^{2}}}

Next Step Prepare to Evaluate

∴

K = \frac{48021.6}{\sqrt{60000^{2} + {(9000.022 \cdot 0.2)}^{2}}}

Next Step Evaluate

∴

K = 0.800000000035223m

LAST Step Rounding Answer

∴

K = 0.8m

Maximum Displacement of Vibration using Force Transmitted Formula Elements

Variables

Functions

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

Force Transmitted

Force Transmitted is the amount of energy transferred from a vibrating system to another system or structure, affecting its motion and stability.

Symbol: F_T

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Force Transmitted

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

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 Maximum Displacement

Go Maximum Displacement of Vibration given Transmissibility Ratio

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

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 Applied Force given Transmissibility Ratio and Maximum Displacement of Vibration

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

Go Applied Force given Transmissibility Ratio

F a = \frac{F T}{ε}

Go Damping Coefficient using Force Transmitted

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

How to Evaluate Maximum Displacement of Vibration using Force Transmitted?

Maximum Displacement of Vibration using Force Transmitted evaluator uses Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)) to evaluate the Maximum Displacement, Maximum Displacement of Vibration using Force Transmitted formula is defined as the maximum amplitude of vibration that occurs in a mechanical system when a force is transmitted, taking into account the stiffness, damping, and frequency of the system, providing a crucial parameter in mechanical vibration analysis. Maximum Displacement is denoted by K symbol.

How to evaluate Maximum Displacement of Vibration using Force Transmitted using this online evaluator? To use this online evaluator for Maximum Displacement of Vibration using Force Transmitted, enter Force Transmitted (F_T), Stiffness of Spring (k), Damping Coefficient (c) & Angular Velocity (ω) and hit the calculate button.

FAQs on Maximum Displacement of Vibration using Force Transmitted

What is the formula to find Maximum Displacement of Vibration using Force Transmitted?

The formula of Maximum Displacement of Vibration using Force Transmitted is expressed as Maximum Displacement = Force Transmitted/(sqrt(Stiffness of Spring^2+(Damping Coefficient*Angular Velocity)^2)). Here is an example- 0.8 = 48021.6/(sqrt(60000^2+(9000.022*0.200022)^2)).

How to calculate Maximum Displacement of Vibration using Force Transmitted?

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

What are the other ways to Calculate Maximum Displacement?

Here are the different ways to Calculate Maximum Displacement-

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

Can the Maximum Displacement of Vibration using Force Transmitted be negative?

No, the Maximum Displacement of Vibration using Force Transmitted, measured in Length cannot be negative.

Which unit is used to measure Maximum Displacement of Vibration using Force Transmitted?

Maximum Displacement of Vibration using Force Transmitted is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Maximum Displacement of Vibration using Force Transmitted can be measured.

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Maximum Displacement of Vibration using Force Transmitted Formula

​GoMaximum Displacement of Vibration given Transmissibility Ratio Formula

Maximum Displacement of Vibration using Force Transmitted Example

Maximum Displacement of Vibration using Force Transmitted Solution

Maximum Displacement of Vibration using Force Transmitted Formula Elements

Other Formulas to find Maximum Displacement

Other formulas in Vibration Isolation and Transmissibility category

How to Evaluate Maximum Displacement of Vibration using Force Transmitted?

FAQs on Maximum Displacement of Vibration using Force Transmitted

Variable Name

GoMaximum Displacement of Vibration given Transmissibility Ratio Formula