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

✖Particular integral is a part of the solution of the differential equation.ⓘ Particular Integral [x₂]			+10% -10%
✖The Complementary Function is a part of the solution of the differential equation.ⓘ Complementary Function [x₁]			+10% -10%

✖Total Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.ⓘ Total Displacement of Forced Vibration given Particular Integral and Complementary Function [d_mass]

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Total Displacement of Forced Vibration given Particular Integral and Complementary Function

Formula

`"d"_{"mass"} = "x"_{"2"}+"x"_{"1"}`

Example

`"14.9m"="12.4m"+"2.5m"`

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Download Frequency of Under Damped Forced Vibrations Formulas PDF

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

STEP 0: Pre-Calculation Summary

Formula Used

Total Displacement = Particular Integral+Complementary Function
d_mass = x₂+x₁
This formula uses 3 Variables

Variables Used

Total Displacement - (Measured in Meter) - Total Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
Particular Integral - (Measured in Meter) - Particular integral is a part of the solution of the differential equation.
Complementary Function - (Measured in Meter) - The Complementary Function is a part of the solution of the differential equation.

STEP 1: Convert Input(s) to Base Unit

Particular Integral: 12.4 Meter --> 12.4 Meter No Conversion Required
Complementary Function: 2.5 Meter --> 2.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_mass = x₂+x₁ --> 12.4+2.5

Evaluating ... ...

d_mass = 14.9

STEP 3: Convert Result to Output's Unit

14.9 Meter --> No Conversion Required

FINAL ANSWER

14.9 Meter <-- Total Displacement

(Calculation completed in 00.006 seconds)

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National Institute Of Technology (NIT), Hamirpur

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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

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

Total Displacement = Particular Integral+Complementary Function
d_mass = x₂+x₁

Why do we need forced vibration?

The vibration of moving vehicle is forced vibration, because the vehicle's engine, springs, the road, etc., continue to make it vibrate. Forced vibration is when an alternating force or motion is applied to a mechanical system, for example when a washing machine shakes due to an imbalance.

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

Total Displacement of Forced Vibration given Particular Integral and Complementary Function calculator uses Total Displacement = Particular Integral+Complementary Function to calculate the Total Displacement, The Total displacement of forced vibration given particular integral and complementary function formula is defined as the complete solution of the differential equation. Total Displacement is denoted by d_mass symbol.

How to calculate Total Displacement of Forced Vibration given Particular Integral and Complementary Function using this online calculator? To use this online calculator for Total Displacement of Forced Vibration given Particular Integral and Complementary Function, enter Particular Integral (x₂) & Complementary Function (x₁) and hit the calculate button. Here is how the Total Displacement of Forced Vibration given Particular Integral and Complementary Function calculation can be explained with given input values -> 14.9 = 12.4+2.5.

FAQ

What is Total Displacement of Forced Vibration given Particular Integral and Complementary Function?

The Total displacement of forced vibration given particular integral and complementary function formula is defined as the complete solution of the differential equation and is represented as d_mass = x₂+x₁ or Total Displacement = Particular Integral+Complementary Function. Particular integral is a part of the solution of the differential equation & The Complementary Function is a part of the solution of the differential equation.

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

The Total displacement of forced vibration given particular integral and complementary function formula is defined as the complete solution of the differential equation is calculated using Total Displacement = Particular Integral+Complementary Function. To calculate Total Displacement of Forced Vibration given Particular Integral and Complementary Function, you need Particular Integral (x₂) & Complementary Function (x₁). With our tool, you need to enter the respective value for Particular Integral & Complementary Function and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Total Displacement?

In this formula, Total Displacement uses Particular Integral & Complementary Function. We can use 5 other way(s) to calculate the same, which is/are as follows -

Total Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
Total Displacement = Static Force/(Mass suspended from Spring*(Natural Circular Frequency^2-Angular Velocity^2))
Total Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity/Stiffness of Spring)^2+(1-(Angular Velocity/Natural Circular Frequency)^2)^2))
Total Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
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))

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