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)/(Standing Wave Height*sqrt([g]/Water Depth))
Tn = (2*pi*X)/(H*sqrt([g]/D))
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 have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.
Maximum Horizontal Particle Excursion - (Measured in Meter) - Maximum Horizontal Particle Excursion at a Node in a standing wave [length].
Standing Wave Height - (Measured in Meter) - Standing Wave Height result when two equal waves are going in opposite direction and in this case you get the usual up/down motion of the water surface but the waves don't progress [length].
Water Depth - (Measured in Meter) - Water depth means 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: 5.1 Meter --> 5.1 Meter No Conversion Required
Standing Wave Height: 5 Meter --> 5 Meter No Conversion Required
Water Depth: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tn = (2*pi*X)/(H*sqrt([g]/D)) --> (2*pi*5.1)/(5*sqrt([g]/12))
Evaluating ... ...
Tn = 7.0894137845068
STEP 3: Convert Result to Output's Unit
7.0894137845068 Second --> No Conversion Required
FINAL ANSWER
7.0894137845068 7.089414 Second <-- Natural Free Oscillating Period of a Basin
(Calculation completed in 00.020 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))*((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 given Maximum Horizontal Particle Excursion at Node Formula

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

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)/(Standing Wave Height*sqrt([g]/Water Depth)) to calculate the Natural Free Oscillating Period of a Basin, Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node, As with closed basins, simplest, classical case is narrow, rectangular basin with uniform depth. basin has vertical walls on three sides and is fully open at one end. fundamental mode of resonant oscillation occurs when there is one-quarter of wave in basin. Natural Free Oscillating Period of a Basin is denoted by Tn 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), Standing Wave Height (H) & Water Depth (D) 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 -> 7.089414 = (2*pi*5.1)/(5*sqrt([g]/12)).

FAQ

What is Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node?
Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node, As with closed basins, simplest, classical case is narrow, rectangular basin with uniform depth. basin has vertical walls on three sides and is fully open at one end. fundamental mode of resonant oscillation occurs when there is one-quarter of wave in basin and is represented as Tn = (2*pi*X)/(H*sqrt([g]/D)) or Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Standing Wave Height*sqrt([g]/Water Depth)). Maximum Horizontal Particle Excursion at a Node in a standing wave [length], Standing Wave Height result when two equal waves are going in opposite direction and in this case you get the usual up/down motion of the water surface but the waves don't progress [length] & Water depth means 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?
Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node, As with closed basins, simplest, classical case is narrow, rectangular basin with uniform depth. basin has vertical walls on three sides and is fully open at one end. fundamental mode of resonant oscillation occurs when there is one-quarter of wave in basin is calculated using Natural Free Oscillating Period of a Basin = (2*pi*Maximum Horizontal Particle Excursion)/(Standing Wave Height*sqrt([g]/Water Depth)). To calculate Natural Free Oscillation period given Maximum Horizontal Particle Excursion at Node, you need Maximum Horizontal Particle Excursion (X), Standing Wave Height (H) & Water Depth (D). With our tool, you need to enter the respective value for Maximum Horizontal Particle Excursion, Standing Wave Height & Water Depth 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, Standing Wave Height & Water Depth. 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 = (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 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 = (Standing Wave Height*Wavelength)/(Average Horizontal Velocity at a Node*pi*Water Depth)
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