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

✖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.ⓘ Particular Integral [x₂]			+10% -10%
✖Complementary Function is a mathematical concept used to solve the differential equation of under damped forced vibrations, providing a complete solution.ⓘ Complementary Function [x₁]			+10% -10%

✖Total displacement in forced vibrations is the sum of the steady-state displacement caused by the external force and any transient displacement.ⓘ Total Displacement of Forced Vibration given Particular Integral and Complementary Function [d_tot]

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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_tot = x₂+x₁
This formula uses 3 Variables

Variables Used

Total Displacement - (Measured in Meter) - Total displacement in forced vibrations is the sum of the steady-state displacement caused by the external force and any transient displacement.
Particular Integral - (Measured in Meter) - 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.
Complementary Function - (Measured in Meter) - Complementary Function is a mathematical concept used to solve the differential equation of under damped forced vibrations, providing a complete solution.

STEP 1: Convert Input(s) to Base Unit

Particular Integral: 0.02 Meter --> 0.02 Meter No Conversion Required
Complementary Function: 1.68 Meter --> 1.68 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_tot = x₂+x₁ --> 0.02+1.68

Evaluating ... ...

d_tot = 1.7

STEP 3: Convert Result to Output's Unit

1.7 Meter --> No Conversion Required

FINAL ANSWER

1.7 Meter <-- Total Displacement

(Calculation completed in 00.004 seconds)

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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

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

LaTeX Go

Total Displacement = Particular Integral+Complementary Function
d_tot = 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, 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 d_tot 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 -> 1.7 = 0.02+1.68.

FAQ

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

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 and is represented as d_tot = x₂+x₁ or Total Displacement = Particular Integral+Complementary Function. 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 & Complementary Function is a mathematical concept used to solve the differential equation of under damped forced vibrations, providing a complete solution.

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 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 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 1 other way(s) to calculate the same, which is/are as follows -

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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