Static Force using Maximum Displacement or Amplitude of Forced Vibration Calculator

✖Maximum displacement refers to the largest distance a vibrating system moves from its equilibrium position during oscillation.ⓘ Maximum Displacement [d_max]			+10% -10%
✖Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force.ⓘ Damping Coefficient [c]			+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%
✖The stiffness of spring is a measure of its resistance to deformation when a force is applied, it quantifies how much the spring compresses or extends in response to a given load.ⓘ Stiffness of Spring [k]			+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%

✖Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations.ⓘ Static Force using Maximum Displacement or Amplitude of Forced Vibration [F_x]

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Static Force using Maximum Displacement or Amplitude of Forced Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Force = Maximum Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))
F_x = d_max*(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 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.
Damping Coefficient - (Measured in Newton Second per Meter) - Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force.
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.
Stiffness of Spring - (Measured in Newton per Meter) - The stiffness of spring is a measure of its resistance to deformation when a force is applied, it quantifies how much the spring compresses or extends in response to a given load.
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.

STEP 1: Convert Input(s) to Base Unit

Maximum Displacement: 0.561 Meter --> 0.561 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

F_x = d_max*(sqrt((c*ω)^2-(k-m*ω^2)^2)) --> 0.561*(sqrt((5*10)^2-(60-0.25*10^2)^2))

Evaluating ... ...

F_x = 20.0317067420627

STEP 3: Convert Result to Output's Unit

20.0317067420627 Newton --> No Conversion Required

FINAL ANSWER

20.0317067420627 ≈ 20.03171 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 using Maximum Displacement or Amplitude of Forced Vibration

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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 using Maximum Displacement or Amplitude of Forced Vibration Formula

LaTeX Go

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

What is Amplitude?

Amplitude is the maximum displacement or distance of a wave or oscillating system from its equilibrium position. It measures the peak value of the oscillation and is a crucial parameter in characterizing waveforms, such as sound waves, light waves, and mechanical vibrations. Amplitude can be expressed in various units, depending on the context, such as meters for mechanical waves or volts for electrical signals.

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 = Maximum Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)) to calculate the Static Force, Static Force using Maximum Displacement or Amplitude of Forced Vibration formula is defined as a measure of the maximum force exerted on an object undergoing forced vibration, taking into account the maximum displacement or amplitude of the vibration, and the frequency of the vibration. Static Force is denoted by F_x 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 Maximum Displacement (d_max), 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 -> 19.996 = 0.561*(sqrt((5*10)^2-(60-0.25*10^2)^2)).

FAQ

What is Static Force using Maximum Displacement or Amplitude of Forced Vibration?

Static Force using Maximum Displacement or Amplitude of Forced Vibration formula is defined as a measure of the maximum force exerted on an object undergoing forced vibration, taking into account the maximum displacement or amplitude of the vibration, and the frequency of the vibration and is represented as F_x = d_max*(sqrt((c*ω)^2-(k-m*ω^2)^2)) or Static Force = Maximum Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)). Maximum displacement refers to the largest distance a vibrating system moves from its equilibrium position during oscillation, Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force, Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis, The stiffness of spring is a measure of its resistance to deformation when a force is applied, it quantifies how much the spring compresses or extends in response to a given load & The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.

How to calculate Static Force using Maximum Displacement or Amplitude of Forced Vibration?

Static Force using Maximum Displacement or Amplitude of Forced Vibration formula is defined as a measure of the maximum force exerted on an object undergoing forced vibration, taking into account the maximum displacement or amplitude of the vibration, and the frequency of the vibration is calculated using Static Force = Maximum 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 Maximum Displacement (d_max), 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 Maximum 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 Maximum 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 = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2)
Static Force = Deflection under Static Force*Stiffness of Spring

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