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Total displacement in forced vibrations is the sum of the steady-state displacement caused by the external force and any transient displacement. Check FAQs
dtot=x2+x1
dtot - Total Displacement?x2 - Particular Integral?x1 - Complementary Function?

Total Displacement of Forced Vibration given Particular Integral and Complementary Function Example

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Here is how the Total Displacement of Forced Vibration given Particular Integral and Complementary Function equation looks like with Values.

Here is how the Total Displacement of Forced Vibration given Particular Integral and Complementary Function equation looks like with Units.

Here is how the Total Displacement of Forced Vibration given Particular Integral and Complementary Function equation looks like.

1.7Edit=0.02Edit+1.68Edit
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Total Displacement of Forced Vibration given Particular Integral and Complementary Function Solution

Follow our step by step solution on how to calculate Total Displacement of Forced Vibration given Particular Integral and Complementary Function?

FIRST Step Consider the formula
dtot=x2+x1
Next Step Substitute values of Variables
∴ dtot=0.02m+1.68m
Next Step Prepare to Evaluate
∴ dtot=0.02+1.68
LAST Step Evaluate
∴dtot=1.7m

Total Displacement of Forced Vibration given Particular Integral and Complementary Function Formula Elements

Variables
Total Displacement
Total displacement in forced vibrations is the sum of the steady-state displacement caused by the external force and any transient displacement.
Symbol: dtot
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Total DisplacementOpen Variable
Particular Integral
Particular Integral is the integral of a function that is used to find the particular solution of a differential equation in under damped forced vibrations.
Symbol: x2
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Particular IntegralOpen Variable
Complementary Function
Complementary Function is a mathematical concept used to solve the differential equation of under damped forced vibrations, providing a complete solution.
Symbol: x1
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Complementary FunctionOpen Variable

Other Formulas to find Total Displacement

​Go Total Displacement of Forced Vibrations
dtot=A⋅cos(ωd-ϕ)+Fx⋅cos(ω⋅tp-ϕ)(c⋅ω)2-(k-m⋅ω2)2

Other formulas in Frequency of Under Damped Forced Vibrations category

​Go Static Force using Maximum Displacement or Amplitude of Forced Vibration
Fx=dmax⋅((c⋅ω)2-(k-m⋅ω2)2)
​Go Static Force when Damping is Negligible
Fx=dmax⋅(m)⋅(ωnat2-ω2)
​Go Deflection of System under Static Force
xo=Fxk
​Go Static Force
Fx=xo⋅k

How to Evaluate Total Displacement of Forced Vibration given Particular Integral and Complementary Function?

Total Displacement of Forced Vibration given Particular Integral and Complementary Function evaluator uses Total Displacement = Particular Integral+Complementary Function to evaluate the Total Displacement, Total Displacement of Forced Vibration given Particular Integral and Complementary Function formula is defined as a measure that combines the particular integral and complementary function to determine the total displacement of a system undergoing forced vibration, providing insight into the system's behavior under external forces. Total Displacement is denoted by dtot symbol.

How to evaluate Total Displacement of Forced Vibration given Particular Integral and Complementary Function using this online evaluator? To use this online evaluator for Total Displacement of Forced Vibration given Particular Integral and Complementary Function, enter Particular Integral (x2) & Complementary Function (x1) and hit the calculate button.

FAQs on Total Displacement of Forced Vibration given Particular Integral and Complementary Function

What is the formula to find Total Displacement of Forced Vibration given Particular Integral and Complementary Function?
The formula of Total Displacement of Forced Vibration given Particular Integral and Complementary Function is expressed as Total Displacement = Particular Integral+Complementary Function. Here is an example- 1.7 = 0.02+1.68.
How to calculate Total Displacement of Forced Vibration given Particular Integral and Complementary Function?
With Particular Integral (x2) & Complementary Function (x1) we can find Total Displacement of Forced Vibration given Particular Integral and Complementary Function using the formula - Total Displacement = Particular Integral+Complementary Function.
What are the other ways to Calculate Total Displacement?
Here are the different ways to Calculate Total Displacement-
  • 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))OpenImg
Can the Total Displacement of Forced Vibration given Particular Integral and Complementary Function be negative?
No, the Total Displacement of Forced Vibration given Particular Integral and Complementary Function, measured in Length cannot be negative.
Which unit is used to measure Total Displacement of Forced Vibration given Particular Integral and Complementary Function?
Total Displacement of Forced Vibration given Particular Integral and Complementary Function is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Total Displacement of Forced Vibration given Particular Integral and Complementary Function can be measured.
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