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Static Force using Maximum Displacement or Amplitude of Forced Vibration Formula

GoStatic Force when Damping is Negligible Formula

GoStatic Force Formula

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Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations. Check FAQs

F x = d max \cdot (\sqrt{{(c \cdot ω)}^{2} - {(k - m \cdot ω^{2})}^{2}})

F_x - Static Force?d_max - Maximum Displacement?c - Damping Coefficient?ω - Angular Velocity?k - Stiffness of Spring?m - Mass suspended from Spring?

Static Force using Maximum Displacement or Amplitude of Forced Vibration Example

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Here is how the Static Force using Maximum Displacement or Amplitude of Forced Vibration equation looks like with Values.

Here is how the Static Force using Maximum Displacement or Amplitude of Forced Vibration equation looks like with Units.

Here is how the Static Force using Maximum Displacement or Amplitude of Forced Vibration equation looks like.

20.0317 = 0.561 \cdot (\sqrt{{(5 \cdot 10)}^{2} - {(60 - 0.25 \cdot 10^{2})}^{2}})

20.0317N = 0.561m \cdot (\sqrt{{(5Ns/m \cdot 10rad/s)}^{2} - {(60N/m - 0.25kg \cdot {10rad/s}^{2})}^{2}})

20.0317 = 0.561 \cdot (\sqrt{{(5 \cdot 10)}^{2} - {(60 - 0.25 \cdot 10^{2})}^{2}})

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Static Force using Maximum Displacement or Amplitude of Forced Vibration Solution

Follow our step by step solution on how to calculate Static Force using Maximum Displacement or Amplitude of Forced Vibration?

FIRST Step Consider the formula

F x = d max \cdot (\sqrt{{(c \cdot ω)}^{2} - {(k - m \cdot ω^{2})}^{2}})

Next Step Substitute values of Variables

∴

F x = 0.561m \cdot (\sqrt{{(5Ns/m \cdot 10rad/s)}^{2} - {(60N/m - 0.25kg \cdot {10rad/s}^{2})}^{2}})

Next Step Prepare to Evaluate

∴

F x = 0.561 \cdot (\sqrt{{(5 \cdot 10)}^{2} - {(60 - 0.25 \cdot 10^{2})}^{2}})

Next Step Evaluate

∴

F x = 20.0317067420627N

LAST Step Rounding Answer

∴

F x = 20.0317N

Static Force using Maximum Displacement or Amplitude of Forced Vibration Formula Elements

Variables

Functions

Static Force

Static Force is the constant force applied to an object undergoing under damped forced vibrations, affecting its frequency of oscillations.

Symbol: F_x

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Static Force

Maximum Displacement

Maximum displacement refers to the largest distance a vibrating system moves from its equilibrium position during oscillation.

Symbol: d_max

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Maximum Displacement

Damping Coefficient

Damping Coefficient is a measure of the rate of decay of oscillations in a system under the influence of an external force.

Symbol: c

Measurement: Damping CoefficientUnit: Ns/m

Note: Value should be greater than 0.

Formulas to find Damping Coefficient

Angular Velocity

Angular velocity is the rate of change of angular displacement over time, describing how fast an object rotates around a point or axis.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

Stiffness of Spring

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.

Symbol: k

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Spring

Mass suspended from Spring

The mass suspended from spring refers to the object attached to a spring that causes the spring to stretch or compress.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass suspended from Spring

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.

Syntax: sqrt(Number)

Other Formulas to find Static Force

Go Static Force when Damping is Negligible

F x = d max \cdot (m) \cdot ({ω nat}^{2} - ω^{2})

Go Static Force

F x = x o \cdot k

Other formulas in Frequency of Under Damped Forced Vibrations category

Go Deflection of System under Static Force

x o = \frac{F x}{k}

Go Maximum Displacement of Forced Vibration at Resonance

d max = x o \cdot \frac{k}{c \cdot ω n}

Go Maximum Displacement of Forced Vibration with Negligible Damping

d max = \frac{F x}{m \cdot ({ω nat}^{2} - ω^{2})}

Go Maximum Displacement of Forced Vibration using Natural Frequency

d max = \frac{x}{\sqrt{\frac{(c^{2}) \cdot (ω^{2})}{k^{2}}} + {(1 - (\frac{ω^{2}}{{ω n}^{2}}))}^{2}}

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

Static Force using Maximum Displacement or Amplitude of Forced Vibration evaluator uses Static Force = Maximum Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)) to evaluate 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 evaluate Static Force using Maximum Displacement or Amplitude of Forced Vibration using this online evaluator? To use this online evaluator 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.

FAQs on Static Force using Maximum Displacement or Amplitude of Forced Vibration

What is the formula to find Static Force using Maximum Displacement or Amplitude of Forced Vibration?

The formula of Static Force using Maximum Displacement or Amplitude of Forced Vibration is expressed as Static Force = Maximum Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)). Here is an example- 19.996 = 0.561*(sqrt((5*10)^2-(60-0.25*10^2)^2)).

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

With Maximum Displacement (d_max), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m) we can find Static Force using Maximum Displacement or Amplitude of Forced Vibration using the formula - Static Force = Maximum Displacement*(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Static Force?

Here are the different ways to Calculate Static Force-

Static Force=Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2)
Static Force=Deflection under Static Force*Stiffness of Spring

Can the Static Force using Maximum Displacement or Amplitude of Forced Vibration be negative?

No, the Static Force using Maximum Displacement or Amplitude of Forced Vibration, measured in Force cannot be negative.

Which unit is used to measure Static Force using Maximum Displacement or Amplitude of Forced Vibration?

Static Force using Maximum Displacement or Amplitude of Forced Vibration is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Static Force using Maximum Displacement or Amplitude of Forced Vibration can be measured.

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Static Force using Maximum Displacement or Amplitude of Forced Vibration Formula

​GoStatic Force when Damping is Negligible Formula

​GoStatic Force Formula

Static Force using Maximum Displacement or Amplitude of Forced Vibration Example

Static Force using Maximum Displacement or Amplitude of Forced Vibration Solution

Static Force using Maximum Displacement or Amplitude of Forced Vibration Formula Elements

Other Formulas to find Static Force

Other formulas in Frequency of Under Damped Forced Vibrations category

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

FAQs on Static Force using Maximum Displacement or Amplitude of Forced Vibration

Variable Name

GoStatic Force when Damping is Negligible Formula

GoStatic Force Formula