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Maximum Displacement from Mean Position given Maximum Potential Energy Formula

GoMaximum Displacement from Mean Position given Maximum Kinetic Energy Formula

GoMaximum Displacement from Mean Position given Maximum Velocity at Mean Position 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 = \sqrt{\frac{2 \cdot PE max}{s constrain}}

x - Maximum Displacement?PE_max - Maximum Potential Energy?s_constrain - Stiffness of Constraint?

Maximum Displacement from Mean Position given Maximum Potential Energy Example

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

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

Here is how the Maximum Displacement from Mean Position given Maximum Potential Energy equation looks like.

1.25 = \sqrt{\frac{2 \cdot 10.1562}{13}}

1.25m = \sqrt{\frac{2 \cdot 10.1562J}{13N/m}}

1.25 = \sqrt{\frac{2 \cdot 10.1562}{13}}

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Maximum Displacement from Mean Position given Maximum Potential Energy Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

x = \sqrt{\frac{2 \cdot 10.1562J}{13N/m}}

Next Step Prepare to Evaluate

∴

x = \sqrt{\frac{2 \cdot 10.1562}{13}}

LAST Step Evaluate

∴

x = 1.25m

Maximum Displacement from Mean Position given Maximum Potential Energy Formula Elements

Variables

Functions

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 Potential Energy

Maximum Potential Energy is the highest energy an object can store when vibrating freely at its natural frequency in a longitudinal direction.

Symbol: PE_max

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Maximum Potential Energy

Stiffness of Constraint

Stiffness of Constraint is the measure of the rigidity of a constraint in a system, affecting the natural frequency of free longitudinal vibrations.

Symbol: s_constrain

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Constraint

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 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 Maximum Velocity at Mean Position

x = \frac{V max}{ω n}

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 Potential Energy?

Maximum Displacement from Mean Position given Maximum Potential Energy evaluator uses Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint) to evaluate the Maximum Displacement, Maximum Displacement from Mean Position given Maximum Potential Energy formula is defined as a measure of the maximum distance an object can move from its mean position when it has maximum potential energy, which is useful in understanding the behavior of objects in free longitudinal vibrations. Maximum Displacement is denoted by x symbol.

How to evaluate Maximum Displacement from Mean Position given Maximum Potential Energy using this online evaluator? To use this online evaluator for Maximum Displacement from Mean Position given Maximum Potential Energy, enter Maximum Potential Energy (PE_max) & Stiffness of Constraint (s_constrain) and hit the calculate button.

FAQs on Maximum Displacement from Mean Position given Maximum Potential Energy

What is the formula to find Maximum Displacement from Mean Position given Maximum Potential Energy?

The formula of Maximum Displacement from Mean Position given Maximum Potential Energy is expressed as Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint). Here is an example- 2.480695 = sqrt((2*10.15625)/13).

How to calculate Maximum Displacement from Mean Position given Maximum Potential Energy?

With Maximum Potential Energy (PE_max) & Stiffness of Constraint (s_constrain) we can find Maximum Displacement from Mean Position given Maximum Potential Energy using the formula - Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Maximum Displacement?

Here are the different ways to Calculate Maximum Displacement-

Maximum Displacement=sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2))
Maximum Displacement=Maximum Velocity/Natural Circular Frequency
Maximum Displacement=(Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))

Can the Maximum Displacement from Mean Position given Maximum Potential Energy be negative?

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

Which unit is used to measure Maximum Displacement from Mean Position given Maximum Potential Energy?

Maximum Displacement from Mean Position given Maximum Potential Energy 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 Potential Energy can be measured.

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Maximum Displacement from Mean Position given Maximum Potential Energy Formula

​GoMaximum Displacement from Mean Position given Maximum Kinetic Energy Formula

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

Maximum Displacement from Mean Position given Maximum Potential Energy Example

Maximum Displacement from Mean Position given Maximum Potential Energy Solution

Maximum Displacement from Mean Position given Maximum Potential Energy 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 Potential Energy?

FAQs on Maximum Displacement from Mean Position given Maximum Potential Energy

Variable Name

GoMaximum Displacement from Mean Position given Maximum Kinetic Energy Formula

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