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Damping Coefficient Formula

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Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force. Check FAQs

c = \frac{\tan (ϕ) \cdot (k - m \cdot ω^{2})}{ω}

c - Damping Coefficient?ϕ - Phase Constant?k - Stiffness of Spring?m - Mass suspended from Spring?ω - Angular Velocity?

Damping Coefficient Example

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

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

Here is how the Damping Coefficient equation looks like.

4.9985 = \frac{\tan (55) \cdot (60 - 0.25 \cdot 10^{2})}{10}

4.9985Ns/m = \frac{\tan (55°) \cdot (60N/m - 0.25kg \cdot {10rad/s}^{2})}{10rad/s}

4.9985 = \frac{\tan (55) \cdot (60 - 0.25 \cdot 10^{2})}{10}

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Damping Coefficient Solution

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

FIRST Step Consider the formula

c = \frac{\tan (ϕ) \cdot (k - m \cdot ω^{2})}{ω}

Next Step Substitute values of Variables

∴

c = \frac{\tan (55°) \cdot (60N/m - 0.25kg \cdot {10rad/s}^{2})}{10rad/s}

Next Step Convert Units

∴

c = \frac{\tan (0.9599rad) \cdot (60N/m - 0.25kg \cdot {10rad/s}^{2})}{10rad/s}

Next Step Prepare to Evaluate

∴

c = \frac{\tan (0.9599) \cdot (60 - 0.25 \cdot 10^{2})}{10}

Next Step Evaluate

∴

c = 4.99851802359548Ns/m

LAST Step Rounding Answer

∴

c = 4.9985Ns/m

Damping Coefficient Formula Elements

Variables

Functions

Damping Coefficient

Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force.

Symbol: c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value should be greater than 0.

Formulas to find Damping Coefficient

Phase Constant

Phase Constant is a measure of the initial displacement or angle of an oscillating system in under damped forced vibrations, affecting its frequency response.

Symbol: ϕ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Phase Constant

Stiffness of Spring

The stiffness of spring is a measure of its resistance to deformation when a force is applied, it quantifies how much the spring compresses or extends in response to a given load.

Symbol: k

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Spring

Mass suspended from Spring

The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass suspended from Spring

Angular Velocity

Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other formulas in Frequency of Under Damped Forced Vibrations category

Go Static Force using Maximum Displacement or Amplitude of Forced Vibration

F x = d max \cdot (\sqrt{{(c \cdot ω)}^{2} - {(k - m \cdot ω^{2})}^{2}})

Go Static Force when Damping is Negligible

F x = d max \cdot (m) \cdot ({ω nat}^{2} - ω^{2})

Go Deflection of System under Static Force

x o = \frac{F x}{k}

Go Static Force

F x = x o \cdot k

How to Evaluate Damping Coefficient?

Damping Coefficient evaluator uses Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity to evaluate the Damping Coefficient, Damping Coefficient formula is defined as a measure of the rate at which the amplitude of oscillations decreases in an underdamped system, providing insight into the energy dissipation in a forced vibration system, particularly in mechanical and electrical systems. Damping Coefficient is denoted by c symbol.

How to evaluate Damping Coefficient using this online evaluator? To use this online evaluator for Damping Coefficient, enter Phase Constant (ϕ), Stiffness of Spring (k), Mass suspended from Spring (m) & Angular Velocity (ω) and hit the calculate button.

FAQs on Damping Coefficient

What is the formula to find Damping Coefficient?

The formula of Damping Coefficient is expressed as Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity. Here is an example- 3.5 = (tan(0.959931088596701)*(60-0.25*10^2))/10.

How to calculate Damping Coefficient?

With Phase Constant (ϕ), Stiffness of Spring (k), Mass suspended from Spring (m) & Angular Velocity (ω) we can find Damping Coefficient using the formula - Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity. This formula also uses Tangent (tan) function(s).

Can the Damping Coefficient be negative?

No, the Damping Coefficient, measured in Damping Coefficient cannot be negative.

Which unit is used to measure Damping Coefficient?

Damping Coefficient 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 can be measured.

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Damping Coefficient Formula

Damping Coefficient Example

Damping Coefficient Solution

Damping Coefficient Formula Elements

Other formulas in Frequency of Under Damped Forced Vibrations category

How to Evaluate Damping Coefficient?

FAQs on Damping Coefficient

Variable Name