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Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node Formula

GoNatural Free Oscillation Period Formula

GoNatural Free Oscillation Period for Average Horizontal Velocity at Node Formula

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Natural Free Oscillating Period of a Basin referred to as the natural period or resonant period, is the time it takes for a wave to travel from one end of the basin to the other and back again. Check FAQs

T n = \frac{2 \cdot π \cdot X}{H wave \cdot \sqrt{\frac{[g]}{D w}}}

T_n - Natural Free Oscillating Period of a Basin?X - Maximum Horizontal Particle Excursion?H_wave - Wave Height?D_w - Depth of Water?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node Example

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Here is how the Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node equation looks like.

5.4106 = \frac{2 \cdot 3.1416 \cdot 7.88}{30 \cdot \sqrt{\frac{9.8066}{105.4}}}

5.4106s = \frac{2 \cdot 3.1416 \cdot 7.88m}{30m \cdot \sqrt{\frac{9.8066m/s²}{105.4m}}}

5.4106 = \frac{2 \cdot 3.1416 \cdot 7.88}{30 \cdot \sqrt{\frac{9.8066}{105.4}}}

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Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node Solution

Follow our step by step solution on how to calculate Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node?

FIRST Step Consider the formula

T n = \frac{2 \cdot π \cdot X}{H wave \cdot \sqrt{\frac{[g]}{D w}}}

Next Step Substitute values of Variables

∴

T n = \frac{2 \cdot π \cdot 7.88m}{30m \cdot \sqrt{\frac{[g]}{105.4m}}}

Next Step Substitute values of Constants

∴

T n = \frac{2 \cdot 3.1416 \cdot 7.88m}{30m \cdot \sqrt{\frac{9.8066m/s²}{105.4m}}}

Next Step Prepare to Evaluate

∴

T n = \frac{2 \cdot 3.1416 \cdot 7.88}{30 \cdot \sqrt{\frac{9.8066}{105.4}}}

Next Step Evaluate

∴

T n = 5.41059215864966s

LAST Step Rounding Answer

∴

T n = 5.4106s

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node Formula Elements

Variables

Constants

Functions

Natural Free Oscillating Period of a Basin

Natural Free Oscillating Period of a Basin referred to as the natural period or resonant period, is the time it takes for a wave to travel from one end of the basin to the other and back again.

Symbol: T_n

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Natural Free Oscillating Period of a Basin

Maximum Horizontal Particle Excursion

Maximum Horizontal Particle Excursion refers to the maximum distance that a particle can travel horizontally from its initial position under the influence of a wave or current.

Symbol: X

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Maximum Horizontal Particle Excursion

Wave Height

Wave Height is formed when two equal waves are going in opposite direction and create the usual up/down motion of the water surface, but the waves don't progress.

Symbol: H_wave

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Wave Height

Depth of Water

Depth of Water is the depth as measured from the water level to the bottom of the considered water body.

Symbol: D_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Water

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Natural Free Oscillating Period of a Basin

Go Natural Free Oscillation Period

T n = (\frac{2}{\sqrt{[g] \cdot d}}) \cdot {({(\frac{n}{l 1})}^{2} + {(\frac{m}{l 2})}^{2})}^{- 0.5}

Go Natural Free Oscillation Period for Average Horizontal Velocity at Node

T n = \frac{H wave \cdot λ}{V' \cdot π \cdot d}

Go Natural Free Oscillation Period for Closed Basin

T n = \frac{2 \cdot L B}{N \cdot \sqrt{[g] \cdot D w}}

Go Natural Free Oscillation Period for Open Basin

T n = 4 \cdot \frac{L B}{(1 + (2 \cdot N)) \cdot \sqrt{[g] \cdot D w}}

Other formulas in Free Oscillation Period category

Go Water Depth given Natural Free Oscillation Period

D = \frac{{(\frac{2 \cdot L hbl}{T n \cdot N})}^{2}}{[g]}

How to Evaluate Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node?

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node evaluator uses Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water)) to evaluate the Natural Free Oscillating Period of a Basin, The Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node formula is defined as the time taken for a wave to complete one full cycle from crest to trough and back to crest. The maximum horizontal particle excursion refers to the greatest horizontal distance a water particle travels from its mean position during wave motion. Natural Free Oscillating Period of a Basin is denoted by T_n symbol.

How to evaluate Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node using this online evaluator? To use this online evaluator for Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node, enter Maximum Horizontal Particle Excursion (X), Wave Height (H_wave) & Depth of Water (D_w) and hit the calculate button.

FAQs on Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node

What is the formula to find Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node?

The formula of Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node is expressed as Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water)). Here is an example- 5.410592 = (2*pi*7.88)/(30*sqrt([g]/105.4)).

How to calculate Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node?

With Maximum Horizontal Particle Excursion (X), Wave Height (H_wave) & Depth of Water (D_w) we can find Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node using the formula - Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water)). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Natural Free Oscillating Period of a Basin?

Here are the different ways to Calculate Natural Free Oscillating Period of a Basin-

Natural Free Oscillating Period of a Basin=(2/sqrt([g]*Water Depth at Harbor))*((Number of Nodes along the X-axis of Basin/Basin Dimensions along the X-axis)^2+(Number of Nodes along the Y-axis of Basin/Basin Dimensions along the Y-axis)^2)^-0.5
Natural Free Oscillating Period of a Basin=(Wave Height*Wavelength)/(Average Horizontal Velocity at a Node*pi*Water Depth at Harbor)
Natural Free Oscillating Period of a Basin=(2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water))

Can the Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node be negative?

Yes, the Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node, measured in Time can be negative.

Which unit is used to measure Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node?

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node can be measured.

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Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node Formula

​GoNatural Free Oscillation Period Formula

​GoNatural Free Oscillation Period for Average Horizontal Velocity at Node Formula

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node Example

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node Solution

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node Formula Elements

Other Formulas to find Natural Free Oscillating Period of a Basin

Other formulas in Free Oscillation Period category

How to Evaluate Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node?

FAQs on Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node

Variable Name

GoNatural Free Oscillation Period Formula

GoNatural Free Oscillation Period for Average Horizontal Velocity at Node Formula