✖Length of Basin along Axis refers to the distance from one end of the basin to the other, typically measured along the longest axis.ⓘ Length of Basin along Axis [L_ba]			+10% -10%
✖Water Depth is the vertical distance from the surface of a water body (such as an ocean, sea, or lake) to the bottom.ⓘ Water Depth [D]			+10% -10%

✖Maximum Oscillation Period refers to the longest time it takes for a system to complete one full cycle of oscillation.ⓘ Maximum Oscillation Period corresponding to Fundamental Mode [T₁]

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Formula

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Maximum Oscillation Period corresponding to Fundamental Mode

Formula

`"T"_{"1"} = 2*"L"_{"ba"}/sqrt("[g]"*"D")`

Example

`"0.013551min"=2*"4.41m"/sqrt("[g]"*"12m")`

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Maximum Oscillation Period corresponding to Fundamental Mode Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Oscillation Period = 2*Length of Basin along Axis/sqrt([g]*Water Depth)
T₁ = 2*L_ba/sqrt([g]*D)
This formula uses 1 Constants, 1 Functions, 3 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

Maximum Oscillation Period - (Measured in Second) - Maximum Oscillation Period refers to the longest time it takes for a system to complete one full cycle of oscillation.
Length of Basin along Axis - (Measured in Meter) - Length of Basin along Axis refers to the distance from one end of the basin to the other, typically measured along the longest axis.
Water Depth - (Measured in Meter) - Water Depth is the vertical distance from the surface of a water body (such as an ocean, sea, or lake) to the bottom.

STEP 1: Convert Input(s) to Base Unit

Length of Basin along Axis: 4.41 Meter --> 4.41 Meter No Conversion Required
Water Depth: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T₁ = 2*L_ba/sqrt([g]*D) --> 2*4.41/sqrt([g]*12)

Evaluating ... ...

T₁ = 0.813050692999644

STEP 3: Convert Result to Output's Unit

0.813050692999644 Second -->0.0135508448833274 Minute (Check conversion here)

FINAL ANSWER

0.0135508448833274 ≈ 0.013551 Minute <-- Maximum Oscillation Period

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Maximum Oscillation Period corresponding to Fundamental Mode

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< 21 Harbor Oscillations Calculators

Additional Length to Account for Mass Outside Each End of Channel

Go Additional Length of the Channel = (-Channel Width corresponding to Mean Water Depth/pi)*ln(pi*Channel Width corresponding to Mean Water Depth/(sqrt([g]*Channel Depth)*Resonant Period for Helmholtz Mode))

Resonant Period for Helmholtz Mode

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))

Maximum Horizontal Particle Excursion at Node

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

Standing Wave Height given Maximum Horizontal Particle Excursion at Node

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

Channel Cross-sectional Area given Resonant Period for Helmholtz Mode

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

Basin Surface Area given Resonant Period for Helmholtz Mode

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

Channel Length for Resonant Period for Helmholtz Mode

Go Channel Length (Helmholtz Mode) = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-Additional Length of the Channel

Additional Length

Go Additional Length of the Channel = ([g]*Cross Sectional Area*(Resonant Period/2*pi)^2/Surface Area)-Channel Length (Helmholtz Mode)

Basin Length along Axis in Open Basin

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

Average Horizontal Velocity at Node

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

Water Depth given Average Horizontal Velocity at Node

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

Standing Wave Height for Average Horizontal Velocity at Node

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

Wave Length for Average Horizontal Velocity at Node

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

Water Depth given Maximum Horizontal Particle Excursion at Node

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

Period for Fundamental Mode

Go Natural Free Oscillating Period of a Basin = (4*Length of Basin along Axis)/sqrt([g]*Water Depth at Harbor)

Basin Length along Axis for given Period of Fundamental Mode

Go Length of Basin along Axis = Natural Free Oscillating Period of a Basin*sqrt([g]*Water Depth at Harbor)/4

Maximum Horizontal Velocity at Node

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

Basin Length along axis given Maximum Oscillation Period corresponding to Fundamental Mode

Go Length of Basin along Axis = Maximum Oscillation Period*sqrt([g]*Water Depth)/2

Maximum Oscillation Period corresponding to Fundamental Mode

Go Maximum Oscillation Period = 2*Length of Basin along Axis/sqrt([g]*Water Depth)

Water Depth for given Period for Fundamental Mode

Go Water Depth at Harbor = ((4*Length of Basin along Axis/Natural Free Oscillating Period of a Basin)^2)/[g]

Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

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

Maximum Oscillation Period corresponding to Fundamental Mode Formula

Maximum Oscillation Period = 2*Length of Basin along Axis/sqrt([g]*Water Depth)
T₁ = 2*L_ba/sqrt([g]*D)

What is Wave Reflection on Structures?

If there is a change in water depth as a wave propagates forward, a portion of the wave’s energy will be reflected. When a wave hits a vertical, impermeable, rigid surface-piercing wall, essentially all of the wave energy will reflect from the wall. On the other hand, when a wave propagates over a small bottom slope, only a very small portion of the energy will be reflected. The degree of wave reflection is defined by the reflection coefficient Cr = Hr/Hi where Hr and Hi are the reflected and incident wave heights, respectively.

How to Calculate Maximum Oscillation Period corresponding to Fundamental Mode?

Maximum Oscillation Period corresponding to Fundamental Mode calculator uses Maximum Oscillation Period = 2*Length of Basin along Axis/sqrt([g]*Water Depth) to calculate the Maximum Oscillation Period, The Maximum Oscillation Period corresponding to Fundamental Mode formula is defined for Closed Basin as a parameter influencing maximum oscillation period T1 corresponding to fundamental mode is given by setting n = 1. Maximum Oscillation Period is denoted by T₁ symbol.

How to calculate Maximum Oscillation Period corresponding to Fundamental Mode using this online calculator? To use this online calculator for Maximum Oscillation Period corresponding to Fundamental Mode, enter Length of Basin along Axis (L_ba) & Water Depth (D) and hit the calculate button. Here is how the Maximum Oscillation Period corresponding to Fundamental Mode calculation can be explained with given input values -> 0.000226 = 2*4.41/sqrt([g]*12).

FAQ

What is Maximum Oscillation Period corresponding to Fundamental Mode?

The Maximum Oscillation Period corresponding to Fundamental Mode formula is defined for Closed Basin as a parameter influencing maximum oscillation period T1 corresponding to fundamental mode is given by setting n = 1 and is represented as T₁ = 2*L_ba/sqrt([g]*D) or Maximum Oscillation Period = 2*Length of Basin along Axis/sqrt([g]*Water Depth). Length of Basin along Axis refers to the distance from one end of the basin to the other, typically measured along the longest axis & Water Depth is the vertical distance from the surface of a water body (such as an ocean, sea, or lake) to the bottom.

How to calculate Maximum Oscillation Period corresponding to Fundamental Mode?

The Maximum Oscillation Period corresponding to Fundamental Mode formula is defined for Closed Basin as a parameter influencing maximum oscillation period T1 corresponding to fundamental mode is given by setting n = 1 is calculated using Maximum Oscillation Period = 2*Length of Basin along Axis/sqrt([g]*Water Depth). To calculate Maximum Oscillation Period corresponding to Fundamental Mode, you need Length of Basin along Axis (L_ba) & Water Depth (D). With our tool, you need to enter the respective value for Length of Basin along Axis & Water Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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