Static Force when Damping is Negligible Calculator

✖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 [d_mass]			+10% -10%
✖A Mass suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter.ⓘ Mass suspended from Spring [m]			+10% -10%
✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Natural Circular Frequency [ω_n]			+10% -10%
✖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.ⓘ Angular Velocity [ω]			+10% -10%

✖Static Force is a force that keeps an object at rest.ⓘ Static Force when Damping is Negligible [F_x]

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Formula

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Static Force when Damping is Negligible

Formula

`"F"_{"x"} = "d"_{"mass"}*("m"*"ω"_{"n"}^2-"ω"^2)`

Example

`"8.2N"="0.8m"*(".25kg"*("21rad/s")^2-("10rad/s")^2)`

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Download Frequency of Under Damped Forced Vibrations Formulas PDF

Static Force when Damping is Negligible Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Force = Total Displacement*(Mass suspended from Spring*Natural Circular Frequency^2-Angular Velocity^2)
F_x = d_mass*(m*ω_n^2-ω^2)
This formula uses 5 Variables

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.
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.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
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.

STEP 1: Convert Input(s) to Base Unit

Total Displacement: 0.8 Meter --> 0.8 Meter No Conversion Required
Mass suspended from Spring: 0.25 Kilogram --> 0.25 Kilogram No Conversion Required
Natural Circular Frequency: 21 Radian per Second --> 21 Radian per Second No Conversion Required
Angular Velocity: 10 Radian per Second --> 10 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_x = d_mass*(m*ω_n^2-ω^2) --> 0.8*(0.25*21^2-10^2)

Evaluating ... ...

F_x = 8.2

STEP 3: Convert Result to Output's Unit

8.2 Newton --> No Conversion Required

FINAL ANSWER

8.2 Newton <-- 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 » Static Force when Damping is Negligible

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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

Static Force when Damping is Negligible Formula

Static Force = Total Displacement*(Mass suspended from Spring*Natural Circular Frequency^2-Angular Velocity^2)
F_x = d_mass*(m*ω_n^2-ω^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 when Damping is Negligible?

Static Force when Damping is Negligible calculator uses Static Force = Total Displacement*(Mass suspended from Spring*Natural Circular Frequency^2-Angular Velocity^2) to calculate the Static Force, The Static force when damping is negligible 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 F_x symbol.

How to calculate Static Force when Damping is Negligible using this online calculator? To use this online calculator for Static Force when Damping is Negligible, enter Total Displacement (d_mass), Mass suspended from Spring (m), Natural Circular Frequency (ω_n) & Angular Velocity (ω) and hit the calculate button. Here is how the Static Force when Damping is Negligible calculation can be explained with given input values -> 30.75 = 0.8*(0.25*21^2-10^2).

FAQ

What is Static Force when Damping is Negligible?

The Static force when damping is negligible 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 F_x = d_mass*(m*ω_n^2-ω^2) or Static Force = Total Displacement*(Mass suspended from Spring*Natural Circular Frequency^2-Angular Velocity^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, A Mass suspended from Spring is defined as the quantitative measure of inertia, a fundamental property of all matter, Natural Circular Frequency is a scalar measure of rotation rate & 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.

How to calculate Static Force when Damping is Negligible?

The Static force when damping is negligible 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*(Mass suspended from Spring*Natural Circular Frequency^2-Angular Velocity^2). To calculate Static Force when Damping is Negligible, you need Total Displacement (d_mass), Mass suspended from Spring (m), Natural Circular Frequency (ω_n) & Angular Velocity (ω). With our tool, you need to enter the respective value for Total Displacement, Mass suspended from Spring, Natural Circular Frequency & Angular Velocity 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, Mass suspended from Spring, Natural Circular Frequency & Angular Velocity. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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