Phase Constant Calculator

✖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]			+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%
✖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%

✖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]

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Phase Constant Solution

STEP 0: Pre-Calculation Summary

Formula Used

Phase Constant = atan((Damping Coefficient*Angular Velocity)/(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))
ϕ = atan((c*ω)/(k-m*ω^2))
This formula uses 2 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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Damping Coefficient: 5 Newton Second per Meter --> 5 Newton Second per Meter No Conversion Required
Angular Velocity: 10 Radian per Second --> 10 Radian per Second No Conversion Required
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ = atan((c*ω)/(k-m*ω^2)) --> atan((5*10)/(60-0.25*10^2))

Evaluating ... ...

ϕ = 0.960070362405688

STEP 3: Convert Result to Output's Unit

0.960070362405688 Radian -->55.0079798014517 Degree (Check conversion here)

FINAL ANSWER

55.0079798014517 ≈ 55.00798 Degree <-- Phase Constant

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Frequency of Under Damped Forced Vibrations » Phase Constant

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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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

Phase Constant Formula

LaTeX Go

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

What is Phase Constant?

The phase constant is a value that indicates the initial angle or phase of a periodic waveform at time zero. It is an essential parameter in oscillatory motion, helping to define the position of the waveform within its cycle. The phase constant is measured in radians and determines how much the waveform is shifted horizontally from a reference point, such as the origin. In the context of simple harmonic motion, it influences the starting position of the oscillating object.

How to Calculate Phase Constant?

Phase Constant calculator uses Phase Constant = atan((Damping Coefficient*Angular Velocity)/(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)) to calculate the Phase Constant, Phase Constant formula is defined as a measure of the initial angle of oscillation in an underdamped forced vibration system, characterizing the phase shift of the oscillations from the driving force, and is a critical parameter in understanding the behavior of oscillatory systems. Phase Constant is denoted by ϕ symbol.

How to calculate Phase Constant using this online calculator? To use this online calculator for Phase Constant, enter Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m) and hit the calculate button. Here is how the Phase Constant calculation can be explained with given input values -> 3151.725 = atan((5*10)/(60-0.25*10^2)).

FAQ

What is Phase Constant?

Phase Constant formula is defined as a measure of the initial angle of oscillation in an underdamped forced vibration system, characterizing the phase shift of the oscillations from the driving force, and is a critical parameter in understanding the behavior of oscillatory systems and is represented as ϕ = atan((c*ω)/(k-m*ω^2)) or Phase Constant = atan((Damping Coefficient*Angular Velocity)/(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)). Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force, Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis, 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.

How to calculate Phase Constant?

Phase Constant formula is defined as a measure of the initial angle of oscillation in an underdamped forced vibration system, characterizing the phase shift of the oscillations from the driving force, and is a critical parameter in understanding the behavior of oscillatory systems is calculated using Phase Constant = atan((Damping Coefficient*Angular Velocity)/(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)). To calculate Phase Constant, you need Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m). With our tool, you need to enter the respective value for Damping Coefficient, Angular Velocity, Stiffness of Spring & Mass suspended from Spring 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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