✖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.ⓘ Maximum Horizontal Particle Excursion [X]			+10% -10%
✖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.ⓘ Wave Height [H_wave]			+10% -10%
✖Depth of Water is the depth as measured from the water level to the bottom of the considered water body.ⓘ Depth of Water [D_w]			+10% -10%

✖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.ⓘ Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node [T_n]

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Formula

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Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node

Formula

`"T"_{"n"} = (2*pi*"X")/("H"_{"wave"}*sqrt("[g]"/"D"_{"w"}))`

Example

`"5.410592s"=(2*pi*"7.88m")/("30.0m"*sqrt("[g]"/"105.4m"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water))
T_n = (2*pi*X)/(H_wave*sqrt([g]/D_w))
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Natural Free Oscillating Period of a Basin - (Measured in Second) - 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.
Maximum Horizontal Particle Excursion - (Measured in Meter) - 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.
Wave Height - (Measured in Meter) - 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.
Depth of Water - (Measured in Meter) - Depth of Water is the depth as measured from the water level to the bottom of the considered water body.

STEP 1: Convert Input(s) to Base Unit

Maximum Horizontal Particle Excursion: 7.88 Meter --> 7.88 Meter No Conversion Required
Wave Height: 30 Meter --> 30 Meter No Conversion Required
Depth of Water: 105.4 Meter --> 105.4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = (2*pi*X)/(H_wave*sqrt([g]/D_w)) --> (2*pi*7.88)/(30*sqrt([g]/105.4))

Evaluating ... ...

T_n = 5.41059215864966

STEP 3: Convert Result to Output's Unit

5.41059215864966 Second --> No Conversion Required

FINAL ANSWER

5.41059215864966 ≈ 5.410592 Second <-- Natural Free Oscillating Period of a Basin

(Calculation completed in 00.004 seconds)

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< 6 Free Oscillation Period Calculators

Natural Free Oscillation Period

Go 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 Oscillation period given Maximum Horizontal Particle Excursion at Node

Go Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water))

Natural Free Oscillation Period for Open Basin

Go Natural Free Oscillating Period of a Basin = 4*Basin Length/((1+(2*Number of Nodes along the Axis of a Basin))*sqrt([g]*Depth of Water))

Natural Free Oscillation Period for Average Horizontal Velocity at Node

Go Natural Free Oscillating Period of a Basin = (Wave Height*Wavelength)/(Average Horizontal Velocity at a Node*pi*Water Depth at Harbor)

Natural Free Oscillation Period for Closed Basin

Go Natural Free Oscillating Period of a Basin = (2*Basin Length)/(Number of Nodes along the Axis of a Basin*sqrt([g]*Depth of Water))

Water Depth given Natural Free Oscillation Period

Go Water Depth = (((2*Harbor Basin Length)/(Natural Free Oscillating Period of a Basin*Number of Nodes along the Axis of a Basin))^2)/[g]

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

Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water))
T_n = (2*pi*X)/(H_wave*sqrt([g]/D_w))

What are Closed Basins?

Enclosed basins can experience oscillations due to a variety of causes. Lake oscillations are usually the result of a sudden change, or a series of intermittent-periodic changes, in atmospheric pressure or wind velocity. Oscillations in canals can be initiated by suddenly adding or subtracting large quantities of water. Harbor oscillations are usually initiated by forcing through the entrance; hence, they deviate from a true closed basin. Local seismic activity can also create oscillations in an enclosed basin.

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

Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node calculator uses Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water)) to calculate 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 calculate Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node using this online calculator? To use this online calculator 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. Here is how the Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node calculation can be explained with given input values -> 5.410592 = (2*pi*7.88)/(30*sqrt([g]/105.4)).

FAQ

What is Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node?

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 and is represented as T_n = (2*pi*X)/(H_wave*sqrt([g]/D_w)) or Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water)). 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, 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 & Depth of Water is the depth as measured from the water level to the bottom of the considered water body.

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

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 is calculated using Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Wave Height*sqrt([g]/Depth of Water)). To calculate Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node, you need Maximum Horizontal Particle Excursion (X), Wave Height (H_wave) & Depth of Water (D_w). With our tool, you need to enter the respective value for Maximum Horizontal Particle Excursion, Wave Height & Depth of Water and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Natural Free Oscillating Period of a Basin?

In this formula, Natural Free Oscillating Period of a Basin uses Maximum Horizontal Particle Excursion, Wave Height & Depth of Water. We can use 4 other way(s) to calculate the same, which is/are as follows -

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))
Natural Free Oscillating Period of a Basin = 4*Basin Length/((1+(2*Number of Nodes along the Axis of a Basin))*sqrt([g]*Depth of Water))

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