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Damping Coefficient using Force Transmitted Formula

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

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

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

Damping Coefficient using Force Transmitted Example

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Here is how the Damping Coefficient using Force Transmitted equation looks like with Values.

Here is how the Damping Coefficient using Force Transmitted equation looks like with Units.

Here is how the Damping Coefficient using Force Transmitted equation looks like.

9000.0224 = \frac{\sqrt{{(\frac{48021.6}{0.8})}^{2} - 60000^{2}}}{0.2}

9000.0224Ns/m = \frac{\sqrt{{(\frac{48021.6N}{0.8m})}^{2} - {60000N/m}^{2}}}{0.2rad/s}

9000.0224 = \frac{\sqrt{{(\frac{48021.6}{0.8})}^{2} - 60000^{2}}}{0.2}

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Damping Coefficient using Force Transmitted Solution

Follow our step by step solution on how to calculate Damping Coefficient using Force Transmitted?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

c = \frac{\sqrt{{(\frac{48021.6N}{0.8m})}^{2} - {60000N/m}^{2}}}{0.2rad/s}

Next Step Prepare to Evaluate

∴

c = \frac{\sqrt{{(\frac{48021.6}{0.8})}^{2} - 60000^{2}}}{0.2}

Next Step Evaluate

∴

c = 9000.02244058349Ns/m

LAST Step Rounding Answer

∴

c = 9000.0224Ns/m

Damping Coefficient using Force Transmitted Formula Elements

Variables

Functions

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

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

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

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 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 Force Transmitted

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

How to Evaluate Damping Coefficient using Force Transmitted?

Damping Coefficient using Force Transmitted evaluator uses Damping Coefficient = (sqrt((Force Transmitted/Maximum Displacement)^2-Stiffness of Spring^2))/Angular Velocity to evaluate the Damping Coefficient, Damping Coefficient using Force Transmitted formula is defined as a measure of the energy dissipation in a mechanical system, specifically in mechanical vibrations, which helps to quantify the reduction in oscillations due to external forces, thereby providing insights into the system's stability and performance. Damping Coefficient is denoted by c symbol.

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

FAQs on Damping Coefficient using Force Transmitted

What is the formula to find Damping Coefficient using Force Transmitted?

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

How to calculate Damping Coefficient using Force Transmitted?

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

Can the Damping Coefficient using Force Transmitted be negative?

No, the Damping Coefficient using Force Transmitted, measured in Damping Coefficient cannot be negative.

Which unit is used to measure Damping Coefficient using Force Transmitted?

Damping Coefficient using Force Transmitted is usually measured using the Newton Second per Meter[Ns/m] for Damping Coefficient. Newton Second per Centimeter[Ns/m] are the few other units in which Damping Coefficient using Force Transmitted can be measured.

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Damping Coefficient using Force Transmitted Formula

Damping Coefficient using Force Transmitted Example

Damping Coefficient using Force Transmitted Solution

Damping Coefficient using Force Transmitted Formula Elements

Other formulas in Vibration Isolation and Transmissibility category

How to Evaluate Damping Coefficient using Force Transmitted?

FAQs on Damping Coefficient using Force Transmitted

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