Damping Coefficient Calculator

✖Phase Constant is a measure of the initial displacement or angle of an oscillating system in under damped forced vibrations, affecting its frequency response.ⓘ Phase Constant [ϕ]			+10% -10%
✖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.ⓘ Stiffness of Spring [k]			+10% -10%
✖The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.ⓘ Mass suspended from Spring [m]			+10% -10%
✖Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.ⓘ Angular Velocity [ω]			+10% -10%

✖Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force.ⓘ Damping Coefficient [c]

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Damping Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity
c = (tan(ϕ)*(k-m*ω^2))/ω
This formula uses 1 Functions, 5 Variables

Functions Used

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., tan(Angle)

Variables Used

Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force.
Phase Constant - (Measured in Radian) - Phase Constant is a measure of the initial displacement or angle of an oscillating system in under damped forced vibrations, affecting its frequency response.
Stiffness of Spring - (Measured in Newton per Meter) - 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.
Mass suspended from Spring - (Measured in Kilogram) - The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.
Angular Velocity - (Measured in Radian per Second) - Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.

STEP 1: Convert Input(s) to Base Unit

Phase Constant: 55 Degree --> 0.959931088596701 Radian (Check conversion here)
Stiffness of Spring: 60 Newton per Meter --> 60 Newton per Meter No Conversion Required
Mass suspended from Spring: 0.25 Kilogram --> 0.25 Kilogram No Conversion Required
Angular Velocity: 10 Radian per Second --> 10 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c = (tan(ϕ)*(k-m*ω^2))/ω --> (tan(0.959931088596701)*(60-0.25*10^2))/10

Evaluating ... ...

c = 4.99851802359548

STEP 3: Convert Result to Output's Unit

4.99851802359548 Newton Second per Meter --> No Conversion Required

FINAL ANSWER

4.99851802359548 ≈ 4.998518 Newton Second per Meter <-- Damping Coefficient

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Frequency of Under Damped Forced Vibrations Calculators

Static Force using Maximum Displacement or Amplitude of Forced Vibration

LaTeX Go Static Force = Maximum Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))

Static Force when Damping is Negligible

LaTeX Go Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2)

Deflection of System under Static Force

LaTeX Go Deflection under Static Force = Static Force/Stiffness of Spring

Static Force

LaTeX Go Static Force = Deflection under Static Force*Stiffness of Spring

Damping Coefficient Formula

LaTeX Go

Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity
c = (tan(ϕ)*(k-m*ω^2))/ω

What is Undamped Free Vibration?

Undamped free vibration refers to the oscillation of a system that occurs without any external forces or energy loss due to friction or air resistance. In this case, the system oscillates at its natural frequency, determined by its mass and stiffness. The amplitude of the vibrations remains constant over time, as there is no energy dissipation. This type of vibration is idealized and helps in understanding the fundamental behavior of vibrating systems. Examples include a mass on a spring or a pendulum swinging in a vacuum.

How to Calculate Damping Coefficient?

Damping Coefficient calculator uses Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity to calculate 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 calculate Damping Coefficient using this online calculator? To use this online calculator for Damping Coefficient, enter Phase Constant (ϕ), Stiffness of Spring (k), Mass suspended from Spring (m) & Angular Velocity (ω) and hit the calculate button. Here is how the Damping Coefficient calculation can be explained with given input values -> 3.5 = (tan(0.959931088596701)*(60-0.25*10^2))/10.

FAQ

What is 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 and is represented as c = (tan(ϕ)*(k-m*ω^2))/ω or Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity. Phase Constant is a measure of the initial displacement or angle of an oscillating system in under damped forced vibrations, affecting its frequency response, 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, The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress & Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.

How to calculate 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 is calculated using Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity. To calculate Damping Coefficient, you need Phase Constant (ϕ), Stiffness of Spring (k), Mass suspended from Spring (m) & Angular Velocity (ω). With our tool, you need to enter the respective value for Phase Constant, Stiffness of Spring, Mass suspended from Spring & Angular Velocity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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