Natural Free Oscillation Period Calculator

✖Water depth means the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [D]			+10% -10%
✖Number of Nodes along the x-axes of Basin.ⓘ Number of Nodes along the x-axes of Basin [n]			+10% -10%
✖Basin Dimensions along the x-axis are the coordinates of the basin along the x-axis.ⓘ Basin Dimensions along the x-axis [l₁]			+10% -10%
✖Number of Nodes along the y-axes of Basin.ⓘ Number of Nodes along the y-axes of Basin [m]			+10% -10%
✖Basin Dimensions along the y-axis are coordinates of the basin along the y axis.ⓘ Basin Dimensions along the y-axis [l₂]			+10% -10%

✖Natural Free Oscillating Period of a Basin have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.ⓘ Natural Free Oscillation Period [T_n]

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Formula

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Natural Free Oscillation Period

Formula

`"T"_{"n"} = (2/sqrt("[g]"*"D"))*(("n"/"l"_{"1"})^2+("m"/"l"_{"2"})^2)^-0.5`

Example

`"0.195549s"=(2/sqrt("[g]"*"12m"))*(("4"/"6m")^2+("2"/"3m")^2)^-0.5`

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Natural Free Oscillation Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Free Oscillating Period of a Basin = (2/sqrt([g]*Water Depth))*((Number of Nodes along the x-axes of Basin/Basin Dimensions along the x-axis)^2+(Number of Nodes along the y-axes of Basin/Basin Dimensions along the y-axis)^2)^-0.5
T_n = (2/sqrt([g]*D))*((n/l₁)^2+(m/l₂)^2)^-0.5
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

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 have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.
Water Depth - (Measured in Meter) - Water depth means the depth as measured from the water level to the bottom of the considered water body.
Number of Nodes along the x-axes of Basin - Number of Nodes along the x-axes of Basin.
Basin Dimensions along the x-axis - (Measured in Meter) - Basin Dimensions along the x-axis are the coordinates of the basin along the x-axis.
Number of Nodes along the y-axes of Basin - Number of Nodes along the y-axes of Basin.
Basin Dimensions along the y-axis - (Measured in Meter) - Basin Dimensions along the y-axis are coordinates of the basin along the y axis.

STEP 1: Convert Input(s) to Base Unit

Water Depth: 12 Meter --> 12 Meter No Conversion Required
Number of Nodes along the x-axes of Basin: 4 --> No Conversion Required
Basin Dimensions along the x-axis: 6 Meter --> 6 Meter No Conversion Required
Number of Nodes along the y-axes of Basin: 2 --> No Conversion Required
Basin Dimensions along the y-axis: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = (2/sqrt([g]*D))*((n/l₁)^2+(m/l₂)^2)^-0.5 --> (2/sqrt([g]*12))*((4/6)^2+(2/3)^2)^-0.5

Evaluating ... ...

T_n = 0.19554886342465

STEP 3: Convert Result to Output's Unit

0.19554886342465 Second --> No Conversion Required

FINAL ANSWER

0.19554886342465 ≈ 0.195549 Second <-- Natural Free Oscillating Period of a Basin

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Free Oscillation Period » Natural Free Oscillation Period

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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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))*((Number of Nodes along the x-axes of Basin/Basin Dimensions along the x-axis)^2+(Number of Nodes along the y-axes 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)/(Standing Wave Height*sqrt([g]/Water Depth))

Natural Free Oscillation Period for Open Basin

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

Natural Free Oscillation Period for Closed Basins

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

Natural Free Oscillation Period for Average Horizontal Velocity at Node

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

Water Depth given Natural Free Oscillation Period

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

Natural Free Oscillation Period Formula

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?

Natural Free Oscillation Period calculator uses Natural Free Oscillating Period of a Basin = (2/sqrt([g]*Water Depth))*((Number of Nodes along the x-axes of Basin/Basin Dimensions along the x-axis)^2+(Number of Nodes along the y-axes of Basin/Basin Dimensions along the y-axis)^2)^-0.5 to calculate the Natural Free Oscillating Period of a Basin, The Natural Free Oscillation Period is defined if the rectangular basin has significant width as well as length, both horizontal dimensions affect the natural period. Natural Free Oscillating Period of a Basin is denoted by T_n symbol.

How to calculate Natural Free Oscillation Period using this online calculator? To use this online calculator for Natural Free Oscillation Period, enter Water Depth (D), Number of Nodes along the x-axes of Basin (n), Basin Dimensions along the x-axis (l₁), Number of Nodes along the y-axes of Basin (m) & Basin Dimensions along the y-axis (l₂) and hit the calculate button. Here is how the Natural Free Oscillation Period calculation can be explained with given input values -> 0.195549 = (2/sqrt([g]*12))*((4/6)^2+(2/3)^2)^-0.5.

FAQ

What is Natural Free Oscillation Period?

The Natural Free Oscillation Period is defined if the rectangular basin has significant width as well as length, both horizontal dimensions affect the natural period and is represented as T_n = (2/sqrt([g]*D))*((n/l₁)^2+(m/l₂)^2)^-0.5 or Natural Free Oscillating Period of a Basin = (2/sqrt([g]*Water Depth))*((Number of Nodes along the x-axes of Basin/Basin Dimensions along the x-axis)^2+(Number of Nodes along the y-axes of Basin/Basin Dimensions along the y-axis)^2)^-0.5. Water depth means the depth as measured from the water level to the bottom of the considered water body, Number of Nodes along the x-axes of Basin, Basin Dimensions along the x-axis are the coordinates of the basin along the x-axis, Number of Nodes along the y-axes of Basin & Basin Dimensions along the y-axis are coordinates of the basin along the y axis.

How to calculate Natural Free Oscillation Period?

The Natural Free Oscillation Period is defined if the rectangular basin has significant width as well as length, both horizontal dimensions affect the natural period is calculated using Natural Free Oscillating Period of a Basin = (2/sqrt([g]*Water Depth))*((Number of Nodes along the x-axes of Basin/Basin Dimensions along the x-axis)^2+(Number of Nodes along the y-axes of Basin/Basin Dimensions along the y-axis)^2)^-0.5. To calculate Natural Free Oscillation Period, you need Water Depth (D), Number of Nodes along the x-axes of Basin (n), Basin Dimensions along the x-axis (l₁), Number of Nodes along the y-axes of Basin (m) & Basin Dimensions along the y-axis (l₂). With our tool, you need to enter the respective value for Water Depth, Number of Nodes along the x-axes of Basin, Basin Dimensions along the x-axis, Number of Nodes along the y-axes of Basin & Basin Dimensions along the y-axis 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 Water Depth, Number of Nodes along the x-axes of Basin, Basin Dimensions along the x-axis, Number of Nodes along the y-axes of Basin & Basin Dimensions along the y-axis. We can use 4 other way(s) to calculate the same, which is/are as follows -

Natural Free Oscillating Period of a Basin = (2*Harbour Basin Length)/(Number of nodes along the Axis of a Basin*sqrt([g]*Water Depth))
Natural Free Oscillating Period of a Basin = 4*Harbour Basin Length/((1+(2*Number of nodes along the Axis of a Basin))*sqrt([g]*Water Depth))
Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Standing Wave Height*sqrt([g]/Water Depth))
Natural Free Oscillating Period of a Basin = (Standing Wave Height*Wavelength)/(Average Horizontal Velocity at a Node*pi*Water Depth)

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