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Maximum Kinetic Energy at Mean Position Formula

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

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

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

Maximum Kinetic Energy at Mean Position Example

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Here is how the Maximum Kinetic Energy at Mean Position equation looks like with Values.

Here is how the Maximum Kinetic Energy at Mean Position equation looks like with Units.

Here is how the Maximum Kinetic Energy at Mean Position equation looks like.

7910.1562 = \frac{5 \cdot 45^{2} \cdot {1.25}^{2}}{2}

7910.1562J = \frac{5kg \cdot {45rad/s}^{2} \cdot {1.25m}^{2}}{2}

7910.1562 = \frac{5 \cdot 45^{2} \cdot {1.25}^{2}}{2}

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Maximum Kinetic Energy at Mean Position Solution

Follow our step by step solution on how to calculate Maximum Kinetic Energy at Mean Position?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

KE = \frac{5 \cdot 45^{2} \cdot {1.25}^{2}}{2}

Next Step Evaluate

∴

KE = 7910.15625J

LAST Step Rounding Answer

∴

KE = 7910.1562J

Maximum Kinetic Energy at Mean Position Formula Elements

Variables

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

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

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 Potential Energy at Mean Position

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

Go Maximum Displacement from Mean Position given Maximum Potential Energy

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

How to Evaluate Maximum Kinetic Energy at Mean Position?

Maximum Kinetic Energy at Mean Position evaluator uses Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2 to evaluate the Maximum Kinetic Energy, Maximum Kinetic Energy at Mean Position formula is defined as the maximum energy an object possesses due to its motion at a mean position, which is a crucial concept in understanding the dynamics of free longitudinal vibrations, particularly in mechanical systems. Maximum Kinetic Energy is denoted by KE symbol.

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

FAQs on Maximum Kinetic Energy at Mean Position

What is the formula to find Maximum Kinetic Energy at Mean Position?

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

How to calculate Maximum Kinetic Energy at Mean Position?

With Load (W_load), Cumulative Frequency (ω_f) & Maximum Displacement (x) we can find Maximum Kinetic Energy at Mean Position using the formula - Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2.

Can the Maximum Kinetic Energy at Mean Position be negative?

No, the Maximum Kinetic Energy at Mean Position, measured in Energy cannot be negative.

Which unit is used to measure Maximum Kinetic Energy at Mean Position?

Maximum Kinetic Energy at Mean Position is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Maximum Kinetic Energy at Mean Position can be measured.

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Maximum Kinetic Energy at Mean Position Formula

Maximum Kinetic Energy at Mean Position Example

Maximum Kinetic Energy at Mean Position Solution

Maximum Kinetic Energy at Mean Position Formula Elements

Other formulas in Rayleigh’s Method category

How to Evaluate Maximum Kinetic Energy at Mean Position?

FAQs on Maximum Kinetic Energy at Mean Position

Variable Name