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Displacement of Body from Mean Position Formula

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Displacement of Body is the maximum distance moved by an object from its mean position during free longitudinal vibrations. Check FAQs

s body = x \cdot \sin (ω n \cdot t total)

s_body - Displacement of Body?x - Maximum Displacement?ω_n - Natural Circular Frequency?t_total - Total Time Taken?

Displacement of Body from Mean Position Example

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Here is how the Displacement of Body from Mean Position equation looks like with Values.

Here is how the Displacement of Body from Mean Position equation looks like with Units.

Here is how the Displacement of Body from Mean Position equation looks like.

0.75 = 1.25 \cdot \sin (21.0044 \cdot 79.9)

0.75m = 1.25m \cdot \sin (21.0044rad/s \cdot 79.9s)

0.75 = 1.25 \cdot \sin (21.0044 \cdot 79.9)

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Displacement of Body from Mean Position Solution

Follow our step by step solution on how to calculate Displacement of Body from Mean Position?

FIRST Step Consider the formula

s body = x \cdot \sin (ω n \cdot t total)

Next Step Substitute values of Variables

∴

s body = 1.25m \cdot \sin (21.0044rad/s \cdot 79.9s)

Next Step Prepare to Evaluate

∴

s body = 1.25 \cdot \sin (21.0044 \cdot 79.9)

Next Step Evaluate

∴

s body = 0.750000447257092m

LAST Step Rounding Answer

∴

s body = 0.75m

Displacement of Body from Mean Position Formula Elements

Variables

Functions

Displacement of Body

Displacement of Body is the maximum distance moved by an object from its mean position during free longitudinal vibrations.

Symbol: s_body

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Displacement of Body

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

Natural Circular Frequency

Natural Circular Frequency is the number of oscillations or cycles per unit time of a free longitudinal vibration in a mechanical system.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular 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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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 Displacement of Body from Mean Position?

Displacement of Body from Mean Position evaluator uses Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken) to evaluate the Displacement of Body, Displacement of Body from Mean Position formula is defined as a measure of the distance of a body from its mean position at a given time in a free longitudinal vibration, providing insight into the oscillatory motion of the body around its equilibrium position. Displacement of Body is denoted by s_body symbol.

How to evaluate Displacement of Body from Mean Position using this online evaluator? To use this online evaluator for Displacement of Body from Mean Position, enter Maximum Displacement (x), Natural Circular Frequency (ω_n) & Total Time Taken (t_total) and hit the calculate button.

FAQs on Displacement of Body from Mean Position

What is the formula to find Displacement of Body from Mean Position?

The formula of Displacement of Body from Mean Position is expressed as Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken). Here is an example- 0.750003 = 1.25*sin(21.00443027*79.9).

How to calculate Displacement of Body from Mean Position?

With Maximum Displacement (x), Natural Circular Frequency (ω_n) & Total Time Taken (t_total) we can find Displacement of Body from Mean Position using the formula - Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken). This formula also uses Sine (sin) function(s).

Can the Displacement of Body from Mean Position be negative?

Yes, the Displacement of Body from Mean Position, measured in Length can be negative.

Which unit is used to measure Displacement of Body from Mean Position?

Displacement of Body from Mean Position is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Displacement of Body from Mean Position can be measured.

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