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Maximum Displacement from Mean Position given Maximum Kinetic Energy Formula

GoMaximum Displacement from Mean Position given Maximum Potential 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 KE}{W load \cdot {ω f}^{2}}}

x - Maximum Displacement?KE - Maximum Kinetic Energy?W_load - Load?ω_f - Cumulative Frequency?

Maximum Displacement from Mean Position given Maximum Kinetic Energy Example

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

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

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

1.25 = \sqrt{\frac{2 \cdot 7910.156}{5 \cdot 45^{2}}}

1.25m = \sqrt{\frac{2 \cdot 7910.156J}{5kg \cdot {45rad/s}^{2}}}

1.25 = \sqrt{\frac{2 \cdot 7910.156}{5 \cdot 45^{2}}}

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Maximum Displacement from Mean Position given Maximum Kinetic Energy Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

x = \sqrt{\frac{2 \cdot 7910.156J}{5kg \cdot {45rad/s}^{2}}}

Next Step Prepare to Evaluate

∴

x = \sqrt{\frac{2 \cdot 7910.156}{5 \cdot 45^{2}}}

Next Step Evaluate

∴

x = 1.24999998024691m

LAST Step Rounding Answer

∴

x = 1.25m

Maximum Displacement from Mean Position given Maximum Kinetic 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 Kinetic Energy

Maximum Kinetic Energy is the highest energy an object can attain during free longitudinal vibrations, typically observed at the natural frequency of oscillation.

Symbol: KE

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Maximum Kinetic Energy

Load

Load is the force or weight applied to an object or structure, typically measured in kilograms, affecting its natural frequency of free longitudinal vibrations.

Symbol: W_load

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Load

Cumulative Frequency

Cumulative Frequency is the total of all frequencies up to a certain value in a dataset, providing insight into the distribution of data.

Symbol: ω_f

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Cumulative Frequency

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 Potential Energy

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

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 Kinetic Energy?

Maximum Displacement from Mean Position given Maximum Kinetic Energy evaluator uses Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2)) to evaluate the Maximum Displacement, Maximum Displacement from Mean Position given Maximum Kinetic Energy formula is defined as a measure of the maximum distance an object can move from its mean position when it has a certain amount of kinetic energy, which is influenced by the load and natural frequency of free longitudinal vibrations. Maximum Displacement is denoted by x symbol.

How to evaluate Maximum Displacement from Mean Position given Maximum Kinetic Energy using this online evaluator? To use this online evaluator for Maximum Displacement from Mean Position given Maximum Kinetic Energy, enter Maximum Kinetic Energy (KE), Load (W_load) & Cumulative Frequency (ω_f) and hit the calculate button.

FAQs on Maximum Displacement from Mean Position given Maximum Kinetic Energy

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

The formula of Maximum Displacement from Mean Position given Maximum Kinetic Energy is expressed as Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2)). Here is an example- 1.25 = sqrt((2*7910.156)/(5*45^2)).

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

With Maximum Kinetic Energy (KE), Load (W_load) & Cumulative Frequency (ω_f) we can find Maximum Displacement from Mean Position given Maximum Kinetic Energy using the formula - Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^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=sqrt((2*Maximum Potential Energy)/Stiffness of Constraint)
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 Kinetic Energy be negative?

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

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

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

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Maximum Displacement from Mean Position given Maximum Kinetic Energy Formula

​GoMaximum Displacement from Mean Position given Maximum Potential Energy Formula

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

Maximum Displacement from Mean Position given Maximum Kinetic Energy Example

Maximum Displacement from Mean Position given Maximum Kinetic Energy Solution

Maximum Displacement from Mean Position given Maximum Kinetic 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 Kinetic Energy?

FAQs on Maximum Displacement from Mean Position given Maximum Kinetic Energy

Variable Name

GoMaximum Displacement from Mean Position given Maximum Potential Energy Formula

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