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Velocity at Mean Position Formula

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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. Check FAQs

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

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

Velocity at Mean Position Example

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Here is how the Velocity at Mean Position equation looks like with Values.

Here is how the Velocity at Mean Position equation looks like with Units.

Here is how the Velocity at Mean Position equation looks like.

2.9682 = (45 \cdot 1.25) \cdot \cos (45 \cdot 79.9)

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

2.9682 = (45 \cdot 1.25) \cdot \cos (45 \cdot 79.9)

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Velocity at Mean Position Solution

Follow our step by step solution on how to calculate Velocity at Mean Position?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

v = (45rad/s \cdot 1.25m) \cdot \cos (45rad/s \cdot 79.9s)

Next Step Prepare to Evaluate

∴

v = (45 \cdot 1.25) \cdot \cos (45 \cdot 79.9)

Next Step Evaluate

∴

v = 2.9681727213244m/s

LAST Step Rounding Answer

∴

v = 2.9682m/s

Velocity at Mean Position Formula Elements

Variables

Functions

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

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

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 in Rayleigh’s Method category

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}

Go Maximum Displacement from Mean Position given Maximum Potential Energy

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

How to Evaluate Velocity at Mean Position?

Velocity at Mean Position evaluator uses Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken) to evaluate the Velocity, Velocity at Mean Position formula is defined as a measure of the velocity of an object at its mean position during free longitudinal vibrations, providing insight into the object's oscillatory behavior and its natural frequency. Velocity is denoted by v symbol.

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

FAQs on Velocity at Mean Position

What is the formula to find Velocity at Mean Position?

The formula of Velocity at Mean Position is expressed as Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken). Here is an example- 2.968173 = (45*1.25)*cos(45*79.9).

How to calculate Velocity at Mean Position?

With Cumulative Frequency (ω_f), Maximum Displacement (x) & Total Time Taken (t_total) we can find Velocity at Mean Position using the formula - Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken). This formula also uses Cosine (cos) function(s).

Can the Velocity at Mean Position be negative?

Yes, the Velocity at Mean Position, measured in Speed can be negative.

Which unit is used to measure Velocity at Mean Position?

Velocity at Mean Position is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Velocity at Mean Position can be measured.

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