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Static Force when Damping is Negligible Formula

GoStatic Force using Maximum Displacement or Amplitude of Forced Vibration 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 (m) \cdot ({ω nat}^{2} - ω^{2})

F_x - Static Force?d_max - Maximum Displacement?m - Mass suspended from Spring?ω_nat - Natural Frequency?ω - Angular Velocity?

Static Force when Damping is Negligible Example

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Here is how the Static Force when Damping is Negligible equation looks like with Values.

Here is how the Static Force when Damping is Negligible equation looks like with Units.

Here is how the Static Force when Damping is Negligible equation looks like.

20 = 0.561 \cdot (0.25) \cdot ({15.5757}^{2} - 10^{2})

20N = 0.561m \cdot (0.25kg) \cdot ({15.5757rad/s}^{2} - {10rad/s}^{2})

20 = 0.561 \cdot (0.25) \cdot ({15.5757}^{2} - 10^{2})

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Static Force when Damping is Negligible Solution

Follow our step by step solution on how to calculate Static Force when Damping is Negligible?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F x = 0.561m \cdot (0.25kg) \cdot ({15.5757rad/s}^{2} - {10rad/s}^{2})

Next Step Prepare to Evaluate

∴

F x = 0.561 \cdot (0.25) \cdot ({15.5757}^{2} - 10^{2})

LAST Step Evaluate

∴

F x = 20N

Static Force when Damping is Negligible Formula Elements

Variables

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

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

Natural Frequency

Natural frequency is the frequency at which a system tends to oscillate when not subjected to external forces.

Symbol: ω_nat

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Frequency

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

Other Formulas to find Static Force

Go Static Force using Maximum Displacement or Amplitude of Forced Vibration

F x = d max \cdot (\sqrt{{(c \cdot ω)}^{2} - {(k - m \cdot ω^{2})}^{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 when Damping is Negligible?

Static Force when Damping is Negligible evaluator uses Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2) to evaluate 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 evaluate Static Force when Damping is Negligible using this online evaluator? To use this online evaluator 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.

FAQs on Static Force when Damping is Negligible

What is the formula to find Static Force when Damping is Negligible?

The formula of Static Force when Damping is Negligible is expressed as Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2). Here is an example- 20.0625 = 0.561*(0.25)*(15.5757020883064^2-10^2).

How to calculate Static Force when Damping is Negligible?

With Maximum Displacement (d_max), Mass suspended from Spring (m), Natural Frequency (ω_nat) & Angular Velocity (ω) we can find Static Force when Damping is Negligible using the formula - Static Force = Maximum Displacement*(Mass suspended from Spring)*(Natural Frequency^2-Angular Velocity^2).

What are the other ways to Calculate Static Force?

Here are the different ways to Calculate Static Force-

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

Can the Static Force when Damping is Negligible be negative?

No, the Static Force when Damping is Negligible, measured in Force cannot be negative.

Which unit is used to measure Static Force when Damping is Negligible?

Static Force when Damping is Negligible is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Static Force when Damping is Negligible can be measured.

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Static Force when Damping is Negligible Formula

​GoStatic Force using Maximum Displacement or Amplitude of Forced Vibration Formula

​GoStatic Force Formula

Static Force when Damping is Negligible Example

Static Force when Damping is Negligible Solution

Static Force when Damping is Negligible Formula Elements

Other Formulas to find Static Force

Other formulas in Frequency of Under Damped Forced Vibrations category

How to Evaluate Static Force when Damping is Negligible?

FAQs on Static Force when Damping is Negligible

Variable Name

GoStatic Force using Maximum Displacement or Amplitude of Forced Vibration Formula

GoStatic Force Formula