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Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Formula

GoMaximum Displacement from Mean Position given Maximum Potential Energy Formula

GoMaximum Displacement from Mean Position given Maximum Kinetic Energy Formula

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Maximum Displacement is the highest distance an object moves from its mean position during free longitudinal vibrations at its natural frequency. Check FAQs

x = \frac{V max}{ω n}

x - Maximum Displacement?V_max - Maximum Velocity?ω_n - Natural Circular Frequency?

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Example

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Here is how the Maximum Displacement from Mean Position given Maximum Velocity at Mean Position equation looks like with Values.

Here is how the Maximum Displacement from Mean Position given Maximum Velocity at Mean Position equation looks like with Units.

Here is how the Maximum Displacement from Mean Position given Maximum Velocity at Mean Position equation looks like.

1.25 = \frac{26.2555}{21.0044}

1.25m = \frac{26.2555m/s}{21.0044rad/s}

1.25 = \frac{26.2555}{21.0044}

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Theory of Machine » fx Maximum Displacement from Mean Position given Maximum Velocity at Mean Position

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Solution

Follow our step by step solution on how to calculate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position?

FIRST Step Consider the formula

x = \frac{V max}{ω n}

Next Step Substitute values of Variables

∴

x = \frac{26.2555m/s}{21.0044rad/s}

Next Step Prepare to Evaluate

∴

x = \frac{26.2555}{21.0044}

Next Step Evaluate

∴

x = 1.24999819859432m

LAST Step Rounding Answer

∴

x = 1.25m

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Formula Elements

Variables

Maximum Displacement

Maximum Displacement is the highest distance an object moves from its mean position during free longitudinal vibrations at its natural frequency.

Symbol: x

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Maximum Displacement

Maximum Velocity

Maximum Velocity is the highest speed achieved by an object undergoing free longitudinal vibrations, typically occurring at the natural frequency of the system.

Symbol: V_max

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Maximum Velocity

Natural Circular Frequency

Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.

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 from Mean Position given Maximum Potential Energy

x = \sqrt{\frac{2 \cdot PE max}{s constrain}}

Go Maximum Displacement from Mean Position given Maximum Kinetic Energy

x = \sqrt{\frac{2 \cdot KE}{W load \cdot {ω f}^{2}}}

Go Maximum Displacement from Mean Position given Velocity at Mean Position

x = \frac{v}{ω f \cdot \cos (ω f \cdot t total)}

Go Maximum Displacement from Mean Position given Displacement of Body from Mean Position

x = \frac{s body}{\sin (ω n \cdot t total)}

Other formulas in Rayleigh’s Method category

Go Velocity at Mean Position

v = (ω f \cdot x) \cdot \cos (ω f \cdot t total)

Go Maximum Velocity at Mean Position by Rayleigh Method

V max = ω n \cdot x

Go Maximum Kinetic Energy at Mean Position

KE = \frac{W load \cdot {ω f}^{2} \cdot x^{2}}{2}

Go Maximum Potential Energy at Mean Position

PE max = \frac{s constrain \cdot x^{2}}{2}

How to Evaluate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position?

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position evaluator uses Maximum Displacement = Maximum Velocity/Natural Circular Frequency to evaluate the Maximum Displacement, Maximum Displacement from Mean Position given Maximum Velocity at Mean Position formula is defined as the maximum distance an object moves from its mean position in a vibrational motion, which is a fundamental concept in the study of free longitudinal vibrations, where the object's velocity and natural frequency are crucial factors. Maximum Displacement is denoted by x symbol.

How to evaluate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position using this online evaluator? To use this online evaluator for Maximum Displacement from Mean Position given Maximum Velocity at Mean Position, enter Maximum Velocity (V_max) & Natural Circular Frequency (ω_n) and hit the calculate button.

FAQs on Maximum Displacement from Mean Position given Maximum Velocity at Mean Position

What is the formula to find Maximum Displacement from Mean Position given Maximum Velocity at Mean Position?

The formula of Maximum Displacement from Mean Position given Maximum Velocity at Mean Position is expressed as Maximum Displacement = Maximum Velocity/Natural Circular Frequency. Here is an example- 1.249998 = 26.2555/21.00443027.

How to calculate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position?

With Maximum Velocity (V_max) & Natural Circular Frequency (ω_n) we can find Maximum Displacement from Mean Position given Maximum Velocity at Mean Position using the formula - Maximum Displacement = Maximum Velocity/Natural Circular Frequency.

What are the other ways to Calculate Maximum Displacement?

Here are the different ways to Calculate Maximum Displacement-

Maximum Displacement=sqrt((2*Maximum Potential Energy)/Stiffness of Constraint)
Maximum Displacement=sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2))
Maximum Displacement=(Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))

Can the Maximum Displacement from Mean Position given Maximum Velocity at Mean Position be negative?

No, the Maximum Displacement from Mean Position given Maximum Velocity at Mean Position, measured in Length cannot be negative.

Which unit is used to measure Maximum Displacement from Mean Position given Maximum Velocity at Mean Position?

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Maximum Displacement from Mean Position given Maximum Velocity at Mean Position can be measured.

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Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Formula

​GoMaximum Displacement from Mean Position given Maximum Potential Energy Formula

​GoMaximum Displacement from Mean Position given Maximum Kinetic Energy Formula

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Example

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Solution

Maximum Displacement from Mean Position given Maximum Velocity at Mean Position Formula Elements

Other Formulas to find Maximum Displacement

Other formulas in Rayleigh’s Method category

How to Evaluate Maximum Displacement from Mean Position given Maximum Velocity at Mean Position?

FAQs on Maximum Displacement from Mean Position given Maximum Velocity at Mean Position

Variable Name

GoMaximum Displacement from Mean Position given Maximum Potential Energy Formula

GoMaximum Displacement from Mean Position given Maximum Kinetic Energy Formula