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Maximum Displacement of Forced Vibration Formula

GoMaximum Displacement of Forced Vibration at Resonance Formula

GoMaximum Displacement of Forced Vibration with Negligible Damping Formula

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

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

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

Maximum Displacement of Forced Vibration Example

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Here is how the Maximum Displacement of Forced Vibration equation looks like with Values.

Here is how the Maximum Displacement of Forced Vibration equation looks like with Units.

Here is how the Maximum Displacement of Forced Vibration equation looks like.

0.5601 = \frac{20}{\sqrt{{(5 \cdot 10)}^{2} - {(60 - 0.25 \cdot 10^{2})}^{2}}}

0.5601m = \frac{20N}{\sqrt{{(5Ns/m \cdot 10rad/s)}^{2} - {(60N/m - 0.25kg \cdot {10rad/s}^{2})}^{2}}}

0.5601 = \frac{20}{\sqrt{{(5 \cdot 10)}^{2} - {(60 - 0.25 \cdot 10^{2})}^{2}}}

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Maximum Displacement of Forced Vibration Solution

Follow our step by step solution on how to calculate Maximum Displacement of Forced Vibration?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d max = \frac{20N}{\sqrt{{(5Ns/m \cdot 10rad/s)}^{2} - {(60N/m - 0.25kg \cdot {10rad/s}^{2})}^{2}}}

Next Step Prepare to Evaluate

∴

d max = \frac{20}{\sqrt{{(5 \cdot 10)}^{2} - {(60 - 0.25 \cdot 10^{2})}^{2}}}

Next Step Evaluate

∴

d max = 0.560112033611204m

LAST Step Rounding Answer

∴

d max = 0.5601m

Maximum Displacement of Forced Vibration Formula Elements

Variables

Functions

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

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

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 Maximum Displacement

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}}

Other formulas in Frequency of Under Damped Forced Vibrations category

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 when Damping is Negligible

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

Go Deflection of System under Static Force

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

Go Static Force

F x = x o \cdot k

How to Evaluate Maximum Displacement of Forced Vibration?

Maximum Displacement of Forced Vibration evaluator uses Maximum Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)) to evaluate the Maximum Displacement, Maximum Displacement of Forced Vibration formula is defined as a measure of the maximum amplitude of an object's oscillation when subjected to an external force, providing insight into the system's response to periodic forces in underdamped systems, commonly observed in mechanical and structural systems. Maximum Displacement is denoted by d_max symbol.

How to evaluate Maximum Displacement of Forced Vibration using this online evaluator? To use this online evaluator for Maximum Displacement of Forced Vibration, enter Static Force (F_x), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m) and hit the calculate button.

FAQs on Maximum Displacement of Forced Vibration

What is the formula to find Maximum Displacement of Forced Vibration?

The formula of Maximum Displacement of Forced Vibration is expressed as Maximum Displacement = Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2)). Here is an example- 0.560112 = 20/(sqrt((5*10)^2-(60-0.25*10^2)^2)).

How to calculate Maximum Displacement of Forced Vibration?

With Static Force (F_x), Damping Coefficient (c), Angular Velocity (ω), Stiffness of Spring (k) & Mass suspended from Spring (m) we can find Maximum Displacement of Forced Vibration using the formula - Maximum Displacement = Static Force/(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 Maximum Displacement?

Here are the different ways to Calculate Maximum Displacement-

Maximum Displacement=Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency)
Maximum Displacement=Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2))
Maximum Displacement=(Deflection)/(sqrt(((Damping Coefficient^2)*(Angular Velocity^2))/(Stiffness of Spring^2))+(1-((Angular Velocity^2)/(Natural Circular Frequency^2)))^2)

Can the Maximum Displacement of Forced Vibration be negative?

No, the Maximum Displacement of Forced Vibration, measured in Length cannot be negative.

Which unit is used to measure Maximum Displacement of Forced Vibration?

Maximum Displacement of Forced Vibration is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Maximum Displacement of Forced Vibration can be measured.

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Maximum Displacement of Forced Vibration Formula

​GoMaximum Displacement of Forced Vibration at Resonance Formula

​GoMaximum Displacement of Forced Vibration with Negligible Damping Formula

Maximum Displacement of Forced Vibration Example

Maximum Displacement of Forced Vibration Solution

Maximum Displacement of Forced Vibration Formula Elements

Other Formulas to find Maximum Displacement

Other formulas in Frequency of Under Damped Forced Vibrations category

How to Evaluate Maximum Displacement of Forced Vibration?

FAQs on Maximum Displacement of Forced Vibration

Variable Name

GoMaximum Displacement of Forced Vibration at Resonance Formula

GoMaximum Displacement of Forced Vibration with Negligible Damping Formula