FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Phase Constant Formula

Fx Copy

LaTeX Copy

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

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

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

Phase Constant Example

With values

With units

Only example

Here is how the Phase Constant equation looks like with Values.

Here is how the Phase Constant equation looks like with Units.

Here is how the Phase Constant equation looks like.

55.008 = a \tan (\frac{5 \cdot 10}{60 - 0.25 \cdot 10^{2}})

55.008° = a \tan (\frac{5Ns/m \cdot 10rad/s}{60N/m - 0.25kg \cdot {10rad/s}^{2}})

55.008 = a \tan (\frac{5 \cdot 10}{60 - 0.25 \cdot 10^{2}})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Machine » fx Phase Constant

Phase Constant Solution

Follow our step by step solution on how to calculate Phase Constant?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ϕ = a \tan (\frac{5Ns/m \cdot 10rad/s}{60N/m - 0.25kg \cdot {10rad/s}^{2}})

Next Step Prepare to Evaluate

∴

ϕ = a \tan (\frac{5 \cdot 10}{60 - 0.25 \cdot 10^{2}})

Next Step Evaluate

∴

ϕ = 0.960070362405688rad

Next Step Convert to Output's Unit

∴

ϕ = 55.0079798014517°

LAST Step Rounding Answer

∴

ϕ = 55.008°

Phase Constant Formula Elements

Variables

Functions

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

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

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

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

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)

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.

Syntax: atan(Number)

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 Phase Constant?

Phase Constant evaluator uses Phase Constant = atan((Damping Coefficient*Angular Velocity)/(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)) to evaluate 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 evaluate Phase Constant using this online evaluator? To use this online evaluator for Phase Constant, enter Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m) and hit the calculate button.

FAQs on Phase Constant

What is the formula to find Phase Constant?

The formula of Phase Constant is expressed as Phase Constant = atan((Damping Coefficient*Angular Velocity)/(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)). Here is an example- 3151.725 = atan((5*10)/(60-0.25*10^2)).

How to calculate Phase Constant?

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

Can the Phase Constant be negative?

No, the Phase Constant, measured in Angle cannot be negative.

Which unit is used to measure Phase Constant?

Phase Constant is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Phase Constant can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Phase Constant Formula

Phase Constant Example

Phase Constant Solution

Phase Constant Formula Elements

Other formulas in Frequency of Under Damped Forced Vibrations category

How to Evaluate Phase Constant?

FAQs on Phase Constant

Variable Name