Static Force using Maximum Displacement or Amplitude of Forced Vibration Solution

STEP 0: Pre-Calculation Summary
Formula Used
Static Force = Total Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
Fx = dmass*(sqrt((c*ω)^2-(k-m*ω^2)^2))
This formula uses 1 Functions, 6 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Static Force - (Measured in Newton) - Static Force is a force that keeps an object at rest.
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.
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.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
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.
Mass suspended from Spring - (Measured in Kilogram) - A Mass suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.
STEP 1: Convert Input(s) to Base Unit
Total Displacement: 0.8 Meter --> 0.8 Meter No Conversion Required
Damping Coefficient: 5 Newton Second per Meter --> 5 Newton Second per Meter No Conversion Required
Angular Velocity: 10 Radian per Second --> 10 Radian per Second No Conversion Required
Stiffness of Spring: 60 Newton per Meter --> 60 Newton per Meter No Conversion Required
Mass suspended from Spring: 0.25 Kilogram --> 0.25 Kilogram No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fx = dmass*(sqrt((c*ω)^2-(k-m*ω^2)^2)) --> 0.8*(sqrt((5*10)^2-(60-0.25*10^2)^2))
Evaluating ... ...
Fx = 28.5657137141714
STEP 3: Convert Result to Output's Unit
28.5657137141714 Newton --> No Conversion Required
FINAL ANSWER
28.5657137141714 28.56571 Newton <-- Static Force
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Indian Institute of Information Technology (IIIT), Guwahati
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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

Static Force using Maximum Displacement or Amplitude of Forced Vibration Formula

Static Force = Total Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
Fx = dmass*(sqrt((c*ω)^2-(k-m*ω^2)^2))

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 Static Force using Maximum Displacement or Amplitude of Forced Vibration?

Static Force using Maximum Displacement or Amplitude of Forced Vibration calculator uses Static Force = Total Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)) to calculate the Static Force, The Static force using maximum displacement or amplitude of forced vibration formula is defined as a force that keeps an object at rest. A static force refers to a constant force applied to a stationary object. Static Force is denoted by Fx symbol.

How to calculate Static Force using Maximum Displacement or Amplitude of Forced Vibration using this online calculator? To use this online calculator for Static Force using Maximum Displacement or Amplitude of Forced Vibration, enter Total Displacement (dmass), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m) and hit the calculate button. Here is how the Static Force using Maximum Displacement or Amplitude of Forced Vibration calculation can be explained with given input values -> 107.1214 = 0.8*(sqrt((5*10)^2-(60-0.25*10^2)^2)).

FAQ

What is Static Force using Maximum Displacement or Amplitude of Forced Vibration?
The Static force using maximum displacement or amplitude of forced vibration formula is defined as a force that keeps an object at rest. A static force refers to a constant force applied to a stationary object and is represented as Fx = dmass*(sqrt((c*ω)^2-(k-m*ω^2)^2)) or Static Force = Total Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)). 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, Damping Coefficient is a material property that indicates whether a material will bounce back or return energy to a system, The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time, Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness & A Mass suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.
How to calculate Static Force using Maximum Displacement or Amplitude of Forced Vibration?
The Static force using maximum displacement or amplitude of forced vibration formula is defined as a force that keeps an object at rest. A static force refers to a constant force applied to a stationary object is calculated using Static Force = Total Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)). To calculate Static Force using Maximum Displacement or Amplitude of Forced Vibration, you need Total Displacement (dmass), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m). With our tool, you need to enter the respective value for Total Displacement, Damping Coefficient, Angular Velocity, Stiffness of Spring & Mass suspended from Spring 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 Static Force?
In this formula, Static Force uses Total Displacement, Damping Coefficient, Angular Velocity, Stiffness of Spring & Mass suspended from Spring. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Static Force = Total Displacement*(Mass suspended from Spring*Natural Circular Frequency^2-Angular Velocity^2)
  • Static Force = Deflection under Static Force*Stiffness of Spring
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