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Maximum Displacement of Forced Vibration with Negligible Damping Formula

GoMaximum Displacement of Forced Vibration at Resonance 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 = \frac{F x}{m \cdot ({ω nat}^{2} - ω^{2})}

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

Maximum Displacement of Forced Vibration with Negligible Damping Example

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

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

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

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

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

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

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Maximum Displacement of Forced Vibration with Negligible Damping Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d max = \frac{20N}{0.25kg \cdot ({15.5757rad/s}^{2} - {10rad/s}^{2})}

Next Step Prepare to Evaluate

∴

d max = \frac{20}{0.25 \cdot ({15.5757}^{2} - 10^{2})}

Next Step Evaluate

∴

d max = 0.560999999999999m

LAST Step Rounding Answer

∴

d max = 0.561m

Maximum Displacement of Forced Vibration with Negligible Damping 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

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

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 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 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 with Negligible Damping?

Maximum Displacement of Forced Vibration with Negligible Damping evaluator uses Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2)) to evaluate the Maximum Displacement, Maximum Displacement of Forced Vibration with Negligible Damping formula is defined as the maximum amplitude of oscillation that occurs in a forced vibration system when the damping force is negligible, providing insight into the system's response to external forces. Maximum Displacement is denoted by d_max symbol.

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

FAQs on Maximum Displacement of Forced Vibration with Negligible Damping

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

The formula of Maximum Displacement of Forced Vibration with Negligible Damping is expressed as Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2)). Here is an example- 0.559252 = 20/(0.25*(15.5757020883064^2-10^2)).

How to calculate Maximum Displacement of Forced Vibration with Negligible Damping?

With Static Force (F_x), Mass suspended from Spring (m), Natural Frequency (ω_nat) & Angular Velocity (ω) we can find Maximum Displacement of Forced Vibration with Negligible Damping using the formula - Maximum Displacement = Static Force/(Mass suspended from Spring*(Natural Frequency^2-Angular Velocity^2)).

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=(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 with Negligible Damping be negative?

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

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

Maximum Displacement of Forced Vibration with Negligible Damping 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 with Negligible Damping can be measured.

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Maximum Displacement of Forced Vibration with Negligible Damping Formula

​GoMaximum Displacement of Forced Vibration at Resonance Formula

​GoMaximum Displacement of Forced Vibration using Natural Frequency Formula

Maximum Displacement of Forced Vibration with Negligible Damping Example

Maximum Displacement of Forced Vibration with Negligible Damping Solution

Maximum Displacement of Forced Vibration with Negligible Damping 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 with Negligible Damping?

FAQs on Maximum Displacement of Forced Vibration with Negligible Damping

Variable Name

GoMaximum Displacement of Forced Vibration at Resonance Formula

GoMaximum Displacement of Forced Vibration using Natural Frequency Formula