Maximum Displacement of Forced Vibration at Resonance Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
dmass = xo*k/(c*ฯ‰n)
This formula uses 5 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.
Deflection under Static Force - (Measured in Meter) - Deflection under Static Force is the deflection of system caused due to static force.
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.
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.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
STEP 1: Convert Input(s) to Base Unit
Deflection under Static Force: 0.33 Meter --> 0.33 Meter No Conversion Required
Stiffness of Spring: 60 Newton per Meter --> 60 Newton per Meter No Conversion Required
Damping Coefficient: 5 Newton Second per Meter --> 5 Newton Second per Meter No Conversion Required
Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dmass = xo*k/(c*ฯ‰n) --> 0.33*60/(5*21)
Evaluating ... ...
dmass = 0.188571428571429
STEP 3: Convert Result to Output's Unit
0.188571428571429 Meter --> No Conversion Required
FINAL ANSWER
0.188571428571429 โ‰ˆ 0.188571 Meter <-- Total Displacement
(Calculation completed in 00.020 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

Maximum Displacement of Forced Vibration at Resonance Formula

Total Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
dmass = xo*k/(c*ฯ‰n)

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 Maximum Displacement of Forced Vibration at Resonance?

Maximum Displacement of Forced Vibration at Resonance calculator uses Total Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency) to calculate the Total Displacement, The Maximum Displacement of Forced Vibration at Resonance formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object. Total Displacement is denoted by dmass symbol.

How to calculate Maximum Displacement of Forced Vibration at Resonance using this online calculator? To use this online calculator for Maximum Displacement of Forced Vibration at Resonance, enter Deflection under Static Force (xo), Stiffness of Spring (k), Damping Coefficient (c) & Natural Circular Frequency (ฯ‰n) and hit the calculate button. Here is how the Maximum Displacement of Forced Vibration at Resonance calculation can be explained with given input values -> 0.188571 = 0.33*60/(5*21).

FAQ

What is Maximum Displacement of Forced Vibration at Resonance?
The Maximum Displacement of Forced Vibration at Resonance formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object and is represented as dmass = xo*k/(c*ฯ‰n) or Total Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency). Deflection under Static Force is the deflection of system caused due to static force, Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness, Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system & Natural Circular Frequency is a scalar measure of rotation rate.
How to calculate Maximum Displacement of Forced Vibration at Resonance?
The Maximum Displacement of Forced Vibration at Resonance formula implies that an object has moved, or has been displaced. Displacement is defined to be the change in position of an object is calculated using Total Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency). To calculate Maximum Displacement of Forced Vibration at Resonance, you need Deflection under Static Force (xo), Stiffness of Spring (k), Damping Coefficient (c) & Natural Circular Frequency (ฯ‰n). With our tool, you need to enter the respective value for Deflection under Static Force, Stiffness of Spring, Damping Coefficient & Natural Circular Frequency 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 Deflection under Static Force, Stiffness of Spring, Damping Coefficient & Natural Circular Frequency. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • 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))
  • Total Displacement = Particular Integral+Complementary Function
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