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 tells you how displaced a wave is from equilibrium or zero position.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Stiffness of Spring - (Measured in Newton per Meter) - Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.
Mass suspended from Spring - (Measured in Kilogram) - A Mass suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.
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 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Dipto Mandal
Indian Institute of Information Technology (IIIT), Guwahati
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15 Frequency of Under Damped Forced Vibrations Calculators

Total Displacement of Forced Vibrations
Go Total Displacement = Amplitude of Vibration*cos(Circular Damped Frequency-Phase Constant)+(Static Force*cos(Angular Velocity*Time Period-Phase Constant))/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
Particular Integral
Go Particular Integral = (Static Force*cos(Angular Velocity*Time Period-Phase Constant))/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
Maximum Displacement of Forced Vibration using Natural Frequency
Go Total Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2))
Static Force using Maximum Displacement or Amplitude of Forced Vibration
Go Static Force = Total Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
Maximum Displacement of Forced Vibration
Go Total Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
Phase Constant
Go Phase Constant = atan((Damping Coefficient*Angular Velocity)/(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))
Damping Coefficient
Go Damping Coefficient = (tan(Phase Constant)*(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2))/Angular Velocity
Maximum Displacement of Forced Vibration at Resonance
Go Total Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
Maximum Displacement of Forced Vibration with Negligible Damping
Go Total Displacement = Static Force/(Mass suspended from Spring*(Natural Circular Frequency^2-Angular Velocity^2))
Static Force when Damping is Negligible
Go Static Force = Total Displacement*(Mass suspended from Spring*Natural Circular Frequency^2-Angular Velocity^2)
Complementary Function
Go Complementary Function = Amplitude of Vibration*cos(Circular Damped Frequency-Phase Constant)
External Periodic Disturbing Force
Go External Periodic Disturbing Force = Static Force*cos(Angular Velocity*Time Period)
Deflection of System under Static Force
Go Deflection under Static Force = Static Force/Stiffness of Spring
Static Force
Go Static Force = Deflection under Static Force*Stiffness of Spring
Total Displacement of Forced Vibration given Particular Integral and Complementary Function
Go Total Displacement = Particular Integral+Complementary Function

Phase Constant Formula

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 undamped free vibration?

The simplest vibrations to analyze are undamped, free, one degree of freedom vibrations. "Undamped" means that there are no energy losses with movement (whether intentional, by adding dampers, or unintentional, through drag or friction). An undamped system will vibrate forever without any additional applied forces.

What is forced vibration?

Forced vibrations occur if a system is continuously driven by an external agency. A simple example is a child's swing that is pushed on each downswing. Of special interest are systems undergoing SHM and driven by sinusoidal forcing.

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, The Phase constant formula tells how much a signal is shifted along the x-axis. A phase constant of ϕ means that each value of the signal happens ϕ amount of time earlier. 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 -> 3604.678 = atan((5*10)/(60-0.25*10^2)).

FAQ

What is Phase Constant?
The Phase constant formula tells how much a signal is shifted along the x-axis. A phase constant of ϕ means that each value of the signal happens ϕ amount of time earlier 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 material property that indicates whether a material will bounce back or return energy to a system, The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time, Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness & A Mass suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.
How to calculate Phase Constant?
The Phase constant formula tells how much a signal is shifted along the x-axis. A phase constant of ϕ means that each value of the signal happens ϕ amount of time earlier 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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