Deflection of System under Static Force Calculator

✖Static Force is a force that keeps an object at rest.ⓘ Static Force [F_x]			+10% -10%
✖Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.ⓘ Stiffness of Spring [k]			+10% -10%

✖Deflection under Static Force is the deflection of system caused due to static force.ⓘ Deflection of System under Static Force [x_o]

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Deflection of System under Static Force

Formula

`"x"_{"o"} = "F"_{"x"}/"k"`

Example

`"0.333333m"="20N"/"60N/m"`

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Download Frequency of Under Damped Forced Vibrations Formulas PDF

Deflection of System under Static Force Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection under Static Force = Static Force/Stiffness of Spring
x_o = F_x/k
This formula uses 3 Variables

Variables Used

Deflection under Static Force - (Measured in Meter) - Deflection under Static Force is the deflection of system caused due to static force.
Static Force - (Measured in Newton) - Static Force is a force that keeps an object at rest.
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.

STEP 1: Convert Input(s) to Base Unit

Static Force: 20 Newton --> 20 Newton No Conversion Required
Stiffness of Spring: 60 Newton per Meter --> 60 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_o = F_x/k --> 20/60

Evaluating ... ...

x_o = 0.333333333333333

STEP 3: Convert Result to Output's Unit

0.333333333333333 Meter --> No Conversion Required

FINAL ANSWER

0.333333333333333 ≈ 0.333333 Meter <-- Deflection under Static Force

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Frequency of Under Damped Forced Vibrations » Deflection of System under Static Force

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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

Deflection of System under Static Force Formula

Deflection under Static Force = Static Force/Stiffness of Spring
x_o = F_x/k

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 Deflection of System under Static Force?

Deflection of System under Static Force calculator uses Deflection under Static Force = Static Force/Stiffness of Spring to calculate the Deflection under Static Force, The Deflection of system under static force formula is defined as the value by which system gets deflected under static force impact. Deflection under Static Force is denoted by x_o symbol.

How to calculate Deflection of System under Static Force using this online calculator? To use this online calculator for Deflection of System under Static Force, enter Static Force (F_x) & Stiffness of Spring (k) and hit the calculate button. Here is how the Deflection of System under Static Force calculation can be explained with given input values -> 0.333333 = 20/60.

FAQ

What is Deflection of System under Static Force?

The Deflection of system under static force formula is defined as the value by which system gets deflected under static force impact and is represented as x_o = F_x/k or Deflection under Static Force = Static Force/Stiffness of Spring. Static Force is a force that keeps an object at rest & Stiffness of Spring is a measure of the resistance offered by an elastic body to deformation. every object in this universe has some stiffness.

How to calculate Deflection of System under Static Force?

The Deflection of system under static force formula is defined as the value by which system gets deflected under static force impact is calculated using Deflection under Static Force = Static Force/Stiffness of Spring. To calculate Deflection of System under Static Force, you need Static Force (F_x) & Stiffness of Spring (k). With our tool, you need to enter the respective value for Static Force & Stiffness of Spring and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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