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Natural Free Oscillation Period Calculator

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Free Oscillation Period Flushing or Circulation Processes and Vessel Interactions Open and Closed Basins

✖Water Depth at Harbor is the vertical distance from the water surface to the seabed or bottom of the harbor.ⓘ Water Depth at Harbor [d]			+10% -10%
✖Number of Nodes along the X-axis of Basin refers to the points where the water surface does not move vertically.ⓘ Number of Nodes along the X-axis of Basin [n]			+10% -10%
✖Basin Dimensions along the X-axis refer to the measurements of a basin or reservoir in the horizontal direction.ⓘ Basin Dimensions along the X-axis [l₁]			+10% -10%
✖Number of Nodes along the y-axis of Basin refers to the points where the water surface does not move vertically along the width of the basin.ⓘ Number of Nodes along the Y-axis of Basin [m]			+10% -10%
✖Basin Dimensions along the Y-axis refer to the measurements of a basin or reservoir in the vertical direction.ⓘ Basin Dimensions along the Y-axis [l₂]			+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 [T_n]

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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 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
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 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.
Water Depth at Harbor - (Measured in Meter) - Water Depth at Harbor is the vertical distance from the water surface to the seabed or bottom of the harbor.
Number of Nodes along the X-axis of Basin - Number of Nodes along the X-axis of Basin refers to the points where the water surface does not move vertically.
Basin Dimensions along the X-axis - (Measured in Meter) - Basin Dimensions along the X-axis refer to the measurements of a basin or reservoir in the horizontal direction.
Number of Nodes along the Y-axis of Basin - Number of Nodes along the y-axis of Basin refers to the points where the water surface does not move vertically along the width of the basin.
Basin Dimensions along the Y-axis - (Measured in Meter) - Basin Dimensions along the Y-axis refer to the measurements of a basin or reservoir in the vertical direction.

STEP 1: Convert Input(s) to Base Unit

Water Depth at Harbor: 1.05 Meter --> 1.05 Meter No Conversion Required
Number of Nodes along the X-axis of Basin: 3 --> No Conversion Required
Basin Dimensions along the X-axis: 35.23 Meter --> 35.23 Meter No Conversion Required
Number of Nodes along the Y-axis of Basin: 2 --> No Conversion Required
Basin Dimensions along the Y-axis: 30.62 Meter --> 30.62 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]*1.05))*((3/35.23)^2+(2/30.62)^2)^-0.5

Evaluating ... ...

T_n = 5.80756281474724

STEP 3: Convert Result to Output's Unit

5.80756281474724 Second --> No Conversion Required

FINAL ANSWER

5.80756281474724 ≈ 5.807563 Second <-- Natural Free Oscillating Period of a Basin

(Calculation completed in 00.020 seconds)

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Coorg Institute of Technology (CIT), Coorg

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< Free Oscillation Period Calculators

Natural Free Oscillation Period

LaTeX 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

LaTeX 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 Average Horizontal Velocity at Node

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

Water Depth given Natural Free Oscillation Period

LaTeX 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]

< Important Formulas of Harbor Oscillation Calculators

Resonant Period for Helmholtz Mode

LaTeX Go Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area of Bay/([g]*Cross Sectional Area))

Standing Wave Height given Maximum Horizontal Velocity at Node

LaTeX Go Standing Wave Height of Ocean = (Maximum Horizontal Velocity at a Node/sqrt([g]/Depth of Water))*2

Maximum Horizontal Velocity at Node

LaTeX Go Maximum Horizontal Velocity at a Node = (Standing Wave Height of Ocean/2)*sqrt([g]/Depth of Water)

Water Depth given Maximum Horizontal Velocity at Node

LaTeX Go Depth of Water = [g]/(Maximum Horizontal Velocity at a Node/(Standing Wave Height of Ocean/2))^2

Natural Free Oscillation Period Formula

LaTeX Go

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 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 to calculate the Natural Free Oscillating Period of a Basin, The Natural Free Oscillation Period formula 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 at Harbor (d), Number of Nodes along the X-axis of Basin (n), Basin Dimensions along the X-axis (l₁), Number of Nodes along the Y-axis 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 -> 4.758255 = (2/sqrt([g]*1.05))*((3/35.23)^2+(2/30.62)^2)^-0.5.

FAQ

What is Natural Free Oscillation Period?

The Natural Free Oscillation Period formula 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 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. Water Depth at Harbor is the vertical distance from the water surface to the seabed or bottom of the harbor, Number of Nodes along the X-axis of Basin refers to the points where the water surface does not move vertically, Basin Dimensions along the X-axis refer to the measurements of a basin or reservoir in the horizontal direction, Number of Nodes along the y-axis of Basin refers to the points where the water surface does not move vertically along the width of the basin & Basin Dimensions along the Y-axis refer to the measurements of a basin or reservoir in the vertical direction.

How to calculate Natural Free Oscillation Period?

The Natural Free Oscillation Period formula 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 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. To calculate Natural Free Oscillation Period, you need Water Depth at Harbor (d), Number of Nodes along the X-axis of Basin (n), Basin Dimensions along the X-axis (l₁), Number of Nodes along the Y-axis of Basin (m) & Basin Dimensions along the Y-axis (l₂). With our tool, you need to enter the respective value for Water Depth at Harbor, Number of Nodes along the X-axis of Basin, Basin Dimensions along the X-axis, Number of Nodes along the Y-axis 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 at Harbor, Number of Nodes along the X-axis of Basin, Basin Dimensions along the X-axis, Number of Nodes along the Y-axis of Basin & Basin Dimensions along the Y-axis. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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