FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Maximum Displacement from Mean Position given Displacement of Body from Mean Position Formula

GoMaximum Displacement from Mean Position given Maximum Potential Energy Formula

GoMaximum Displacement from Mean Position given Maximum Kinetic Energy Formula

Fx Copy

LaTeX Copy

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{s body}{\sin (ω n \cdot t total)}

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

Maximum Displacement from Mean Position given Displacement of Body from Mean Position Example

With values

With units

Only example

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

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

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

1.25 = \frac{0.75}{\sin (21.0044 \cdot 79.9)}

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

1.25 = \frac{0.75}{\sin (21.0044 \cdot 79.9)}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Machine » fx Maximum Displacement from Mean Position given Displacement of Body from Mean Position

Maximum Displacement from Mean Position given Displacement of Body from Mean Position Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

x = \frac{0.75m}{\sin (21.0044rad/s \cdot 79.9s)}

Next Step Prepare to Evaluate

∴

x = \frac{0.75}{\sin (21.0044 \cdot 79.9)}

Next Step Evaluate

∴

x = 1.24999925457196m

LAST Step Rounding Answer

∴

x = 1.25m

Maximum Displacement from Mean Position given Displacement of Body from 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

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

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 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 Velocity at Mean Position

x = \frac{v}{ω f \cdot \cos (ω f \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 Displacement of Body from Mean Position?

Maximum Displacement from Mean Position given Displacement of Body from Mean Position evaluator uses Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken)) to evaluate the Maximum Displacement, Maximum Displacement from Mean Position given Displacement of Body from Mean Position formula is defined as the maximum distance of an object from its mean position during free longitudinal vibrations, which is a fundamental concept in physics to understand the oscillatory motion of objects. Maximum Displacement is denoted by x symbol.

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

FAQs on Maximum Displacement from Mean Position given Displacement of Body from Mean Position

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

The formula of Maximum Displacement from Mean Position given Displacement of Body from Mean Position is expressed as Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken)). Here is an example- 1.249995 = 0.75/(sin(21.00443027*79.9)).

How to calculate Maximum Displacement from Mean Position given Displacement of Body from Mean Position?

With Displacement of Body (s_body), Natural Circular Frequency (ω_n) & Total Time Taken (t_total) we can find Maximum Displacement from Mean Position given Displacement of Body from Mean Position using the formula - Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken)). This formula also uses Sine (sin) 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 Displacement of Body from Mean Position be negative?

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

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

Maximum Displacement from Mean Position given 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 Maximum Displacement from Mean Position given Displacement of Body from Mean Position can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit