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Maximum Displacement of Forced Vibration at Resonance Formula

GoMaximum Displacement of Forced Vibration with Negligible Damping Formula

GoMaximum Displacement of Forced Vibration using Natural Frequency 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 = x o \cdot \frac{k}{c \cdot ω n}

d_max - Maximum Displacement?x_o - Deflection under Static Force?k - Stiffness of Spring?c - Damping Coefficient?ω_n - Natural Circular Frequency?

Maximum Displacement of Forced Vibration at Resonance Example

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

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

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

0.561 = 0.3333 \cdot \frac{60}{5 \cdot 7.13}

0.561m = 0.3333m \cdot \frac{60N/m}{5Ns/m \cdot 7.13rad/s}

0.561 = 0.3333 \cdot \frac{60}{5 \cdot 7.13}

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Maximum Displacement of Forced Vibration at Resonance Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d max = 0.3333m \cdot \frac{60N/m}{5Ns/m \cdot 7.13rad/s}

Next Step Prepare to Evaluate

∴

d max = 0.3333 \cdot \frac{60}{5 \cdot 7.13}

Next Step Evaluate

∴

d max = 0.561009761570828m

LAST Step Rounding Answer

∴

d max = 0.561m

Maximum Displacement of Forced Vibration at Resonance Formula Elements

Variables

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

Deflection under Static Force

Deflection under static force refers to the displacement or deformation of a structure or object when subjected to a constant, unchanging force.

Symbol: x_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Deflection under Static Force

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

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

Natural Circular Frequency

Natural Circular Frequency is the frequency at which a system tends to oscillate in the absence of any external force.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular Frequency

Other Formulas to find Maximum Displacement

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}}

Go Maximum Displacement of Forced Vibration

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

Maximum Displacement of Forced Vibration at Resonance evaluator uses Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency) to evaluate the Maximum Displacement, Maximum Displacement of Forced Vibration at Resonance formula is defined as the maximum amplitude of oscillation that occurs in a vibrating system when the frequency of the external force matches the natural frequency of the system, resulting in the largest possible displacement. Maximum Displacement is denoted by d_max symbol.

How to evaluate Maximum Displacement of Forced Vibration at Resonance using this online evaluator? To use this online evaluator for Maximum Displacement of Forced Vibration at Resonance, enter Deflection under Static Force (x_o), Stiffness of Spring (k), Damping Coefficient (c) & Natural Circular Frequency (ω_n) and hit the calculate button.

FAQs on Maximum Displacement of Forced Vibration at Resonance

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

The formula of Maximum Displacement of Forced Vibration at Resonance is expressed as Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency). Here is an example- 0.258198 = 0.3333333*60/(5*7.13).

How to calculate Maximum Displacement of Forced Vibration at Resonance?

With Deflection under Static Force (x_o), Stiffness of Spring (k), Damping Coefficient (c) & Natural Circular Frequency (ω_n) we can find Maximum Displacement of Forced Vibration at Resonance using the formula - Maximum Displacement = Deflection under Static Force*Stiffness of Spring/(Damping Coefficient*Natural Circular Frequency).

What are the other ways to Calculate Maximum Displacement?

Here are the different ways to Calculate Maximum Displacement-

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)
Maximum Displacement=Static Force/(sqrt((Damping Coefficient*Angular Velocity)^2-(Stiffness of Spring-Mass suspended from Spring*Angular Velocity^2)^2))

Can the Maximum Displacement of Forced Vibration at Resonance be negative?

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

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

Maximum Displacement of Forced Vibration at Resonance 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 at Resonance can be measured.

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Maximum Displacement of Forced Vibration at Resonance Formula

​GoMaximum Displacement of Forced Vibration with Negligible Damping Formula

​GoMaximum Displacement of Forced Vibration using Natural Frequency Formula

Maximum Displacement of Forced Vibration at Resonance Example

Maximum Displacement of Forced Vibration at Resonance Solution

Maximum Displacement of Forced Vibration at Resonance 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 at Resonance?

FAQs on Maximum Displacement of Forced Vibration at Resonance

Variable Name

GoMaximum Displacement of Forced Vibration with Negligible Damping Formula

GoMaximum Displacement of Forced Vibration using Natural Frequency Formula