Static Force when Damping is Negligible Calculator

✖Maximum displacement refers to the largest distance a vibrating system moves from its equilibrium position during oscillation.ⓘ Maximum Displacement [d_max]			+10% -10%
✖The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.ⓘ Mass suspended from Spring [m]			+10% -10%
✖Natural frequency is the frequency at which a system tends to oscillate when not subjected to external forces.ⓘ Natural Frequency [ω_nat]			+10% -10%
✖Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.ⓘ Angular Velocity [ω]			+10% -10%

✖Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations.ⓘ Static Force when Damping is Negligible [F_x]

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Static Force when Damping is Negligible Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2)
F_x = d_max*(m)*(ω_nat^2-ω^2)
This formula uses 5 Variables

Variables Used

Static Force - (Measured in Newton) - Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations.
Maximum Displacement - (Measured in Meter) - Maximum displacement refers to the largest distance a vibrating system moves from its equilibrium position during oscillation.
Mass suspended from Spring - (Measured in Kilogram) - The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.
Natural Frequency - (Measured in Radian per Second) - Natural frequency is the frequency at which a system tends to oscillate when not subjected to external forces.
Angular Velocity - (Measured in Radian per Second) - Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.

STEP 1: Convert Input(s) to Base Unit

Maximum Displacement: 0.561 Meter --> 0.561 Meter No Conversion Required
Mass suspended from Spring: 0.25 Kilogram --> 0.25 Kilogram No Conversion Required
Natural Frequency: 15.5757020883064 Radian per Second --> 15.5757020883064 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_max*(m)*(ω_nat^2-ω^2) --> 0.561*(0.25)*(15.5757020883064^2-10^2)

Evaluating ... ...

F_x = 20

STEP 3: Convert Result to Output's Unit

20 Newton --> No Conversion Required

FINAL ANSWER

20 Newton <-- Static Force

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Frequency of Under Damped Forced Vibrations » Static Force when Damping is Negligible

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National Institute Of Technology (NIT), Hamirpur

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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

Static Force when Damping is Negligible Formula

LaTeX Go

Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2)
F_x = d_max*(m)*(ω_nat^2-ω^2)

What is Damping Ratio?

The damping ratio is a dimensionless measure that indicates the level of damping in a vibrating system compared to critical damping. It is calculated as the ratio of actual damping to critical damping, which is the minimum required to prevent oscillation. A damping ratio less than one signifies underdamping, resulting in oscillations with decreasing amplitude. A ratio of one indicates critical damping, where the system returns to equilibrium without oscillating. A ratio greater than one denotes overdamping, where the system returns to equilibrium slowly and without oscillation.

How to Calculate Static Force when Damping is Negligible?

Static Force when Damping is Negligible calculator uses Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2) to calculate the Static Force, Static Force when Damping is Negligible formula is defined as a measure of the maximum force exerted on an object in a vibrational system when the damping force is negligible, providing insight into the system's oscillatory behavior and its response to external forces. 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 Maximum Displacement (d_max), Mass suspended from Spring (m), Natural Frequency (ω_nat) & 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 -> 20.0625 = 0.561*(0.25)*(15.5757020883064^2-10^2).

FAQ

What is Static Force when Damping is Negligible?

Static Force when Damping is Negligible formula is defined as a measure of the maximum force exerted on an object in a vibrational system when the damping force is negligible, providing insight into the system's oscillatory behavior and its response to external forces and is represented as F_x = d_max*(m)*(ω_nat^2-ω^2) or Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2). Maximum displacement refers to the largest distance a vibrating system moves from its equilibrium position during oscillation, The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress, Natural frequency is the frequency at which a system tends to oscillate when not subjected to external forces & Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.

How to calculate Static Force when Damping is Negligible?

Static Force when Damping is Negligible formula is defined as a measure of the maximum force exerted on an object in a vibrational system when the damping force is negligible, providing insight into the system's oscillatory behavior and its response to external forces is calculated using Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2). To calculate Static Force when Damping is Negligible, you need Maximum Displacement (d_max), Mass suspended from Spring (m), Natural Frequency (ω_nat) & Angular Velocity (ω). With our tool, you need to enter the respective value for Maximum Displacement, Mass suspended from Spring, Natural 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 Maximum Displacement, Mass suspended from Spring, Natural Frequency & Angular Velocity. We can use 2 other way(s) to calculate the same, which is/are as follows -

Static Force = Maximum 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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