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Maximum Displacement from Mean Position given 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}{ω f \cdot \cos (ω f \cdot t total)}

x - Maximum Displacement?v - Velocity?ω_f - Cumulative Frequency?t_total - Total Time Taken?

Maximum Displacement from Mean Position given Velocity at Mean Position Example

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

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

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

1.25 = \frac{2.9682}{45 \cdot \cos (45 \cdot 79.9)}

1.25m = \frac{2.9682m/s}{45rad/s \cdot \cos (45rad/s \cdot 79.9s)}

1.25 = \frac{2.9682}{45 \cdot \cos (45 \cdot 79.9)}

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Maximum Displacement from Mean Position given Velocity at Mean Position Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

x = \frac{2.9682m/s}{45rad/s \cdot \cos (45rad/s \cdot 79.9s)}

Next Step Prepare to Evaluate

∴

x = \frac{2.9682}{45 \cdot \cos (45 \cdot 79.9)}

Next Step Evaluate

∴

x = 1.25000011735992m

LAST Step Rounding Answer

∴

x = 1.25m

Maximum Displacement from Mean Position given Velocity at Mean Position 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

Velocity

Velocity is the rate of change of an object's position with respect to time during free longitudinal vibrations, describing the oscillatory motion of an object.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity

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

Total Time Taken

Total Time Taken is the time required for an object to complete one free longitudinal vibration under natural frequency without any external force.

Symbol: t_total

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Total Time Taken

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

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 Maximum Velocity at Mean Position

x = \frac{V max}{ω n}

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 Velocity at Mean Position?

Maximum Displacement from Mean Position given Velocity at Mean Position evaluator uses Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken)) to evaluate the Maximum Displacement, Maximum Displacement from Mean Position given Velocity at Mean Position formula is defined as the maximum distance of an object from its mean position in a vibrational motion, which is a critical parameter in understanding the dynamics of free longitudinal vibrations, particularly in the context of natural frequency. Maximum Displacement is denoted by x symbol.

How to evaluate Maximum Displacement from Mean Position given Velocity at Mean Position using this online evaluator? To use this online evaluator for Maximum Displacement from Mean Position given Velocity at Mean Position, enter Velocity (v), Cumulative Frequency (ω_f) & Total Time Taken (t_total) and hit the calculate button.

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

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

The formula of Maximum Displacement from Mean Position given Velocity at Mean Position is expressed as Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken)). Here is an example- 25.26807 = (2.968173)/(45*cos(45*79.9)).

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

With Velocity (v), Cumulative Frequency (ω_f) & Total Time Taken (t_total) we can find Maximum Displacement from Mean Position given Velocity at Mean Position using the formula - Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken)). This formula also uses Cosine (cos) 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=sqrt((2*Maximum Kinetic Energy)/(Load*Cumulative Frequency^2))
Maximum Displacement=Maximum Velocity/Natural Circular Frequency

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

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

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

Maximum Displacement from Mean Position given 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 Velocity at Mean Position can be measured.

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