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Natural Free Oscillation Period Formula

GoNatural Free Oscillation Period for Closed Basin Formula

GoNatural Free Oscillation Period for Open Basin Formula

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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. Check FAQs

T n = (\frac{2}{\sqrt{[g] \cdot d}}) \cdot {({(\frac{n}{l 1})}^{2} + {(\frac{m}{l 2})}^{2})}^{- 0.5}

T_n - Natural Free Oscillating Period of a Basin?d - Water Depth at Harbor?n - Number of Nodes along the X-axis of Basin?l₁ - Basin Dimensions along the X-axis?m - Number of Nodes along the Y-axis of Basin?l₂ - Basin Dimensions along the Y-axis?[g] - Gravitational acceleration on Earth?

Natural Free Oscillation Period Example

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Here is how the Natural Free Oscillation Period equation looks like with Values.

Here is how the Natural Free Oscillation Period equation looks like with Units.

Here is how the Natural Free Oscillation Period equation looks like.

5.8076 = (\frac{2}{\sqrt{9.8066 \cdot 1.05}}) \cdot {({(\frac{3}{35.23})}^{2} + {(\frac{2}{30.62})}^{2})}^{- 0.5}

5.8076s = (\frac{2}{\sqrt{9.8066m/s² \cdot 1.05m}}) \cdot {({(\frac{3}{35.23m})}^{2} + {(\frac{2}{30.62m})}^{2})}^{- 0.5}

5.8076 = (\frac{2}{\sqrt{9.8066 \cdot 1.05}}) \cdot {({(\frac{3}{35.23})}^{2} + {(\frac{2}{30.62})}^{2})}^{- 0.5}

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Natural Free Oscillation Period Solution

Follow our step by step solution on how to calculate Natural Free Oscillation Period?

FIRST Step Consider the formula

T n = (\frac{2}{\sqrt{[g] \cdot d}}) \cdot {({(\frac{n}{l 1})}^{2} + {(\frac{m}{l 2})}^{2})}^{- 0.5}

Next Step Substitute values of Variables

∴

T n = (\frac{2}{\sqrt{[g] \cdot 1.05m}}) \cdot {({(\frac{3}{35.23m})}^{2} + {(\frac{2}{30.62m})}^{2})}^{- 0.5}

Next Step Substitute values of Constants

∴

T n = (\frac{2}{\sqrt{9.8066m/s² \cdot 1.05m}}) \cdot {({(\frac{3}{35.23m})}^{2} + {(\frac{2}{30.62m})}^{2})}^{- 0.5}

Next Step Prepare to Evaluate

∴

T n = (\frac{2}{\sqrt{9.8066 \cdot 1.05}}) \cdot {({(\frac{3}{35.23})}^{2} + {(\frac{2}{30.62})}^{2})}^{- 0.5}

Next Step Evaluate

∴

T n = 5.80756281474724s

LAST Step Rounding Answer

∴

T n = 5.8076s

Natural Free Oscillation Period Formula Elements

Variables

Constants

Functions

Natural Free Oscillating Period of a Basin

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.

Symbol: T_n

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Natural Free Oscillating Period of a Basin

Water Depth at Harbor

Water Depth at Harbor is the vertical distance from the water surface to the seabed or bottom of the harbor.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Water Depth at 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.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Nodes along the X-axis of Basin

Basin Dimensions along the X-axis

Basin Dimensions along the X-axis refer to the measurements of a basin or reservoir in the horizontal direction.

Symbol: l₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Basin Dimensions along the X-axis

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.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Nodes along the Y-axis of Basin

Basin Dimensions along the Y-axis

Basin Dimensions along the Y-axis refer to the measurements of a basin or reservoir in the vertical direction.

Symbol: l₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Basin Dimensions along the Y-axis

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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.

Syntax: sqrt(Number)

Other Formulas to find Natural Free Oscillating Period of a Basin

Go Natural Free Oscillation Period for Closed Basin

T n = \frac{2 \cdot L B}{N \cdot \sqrt{[g] \cdot D w}}

Go Natural Free Oscillation Period for Open Basin

T n = 4 \cdot \frac{L B}{(1 + (2 \cdot N)) \cdot \sqrt{[g] \cdot D w}}

Other formulas in Free Oscillation Period category

Go Maximum Horizontal Velocity at Node

V max = (\frac{H w}{2}) \cdot \sqrt{\frac{[g]}{D w}}

Go Standing Wave Height given Maximum Horizontal Velocity at Node

H w = (\frac{V max}{\sqrt{\frac{[g]}{D w}}}) \cdot 2

Go Water Depth given Maximum Horizontal Velocity at Node

D w = \frac{[g]}{{(\frac{V max}{\frac{H w}{2}})}^{2}}

Go Resonant Period for Helmholtz Mode

T H = (2 \cdot π) \cdot \sqrt{(L ch + l' c) \cdot \frac{A b}{[g] \cdot A C}}

How to Evaluate Natural Free Oscillation Period?

Natural Free Oscillation Period evaluator 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 evaluate 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 evaluate Natural Free Oscillation Period using this online evaluator? To use this online evaluator 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.

FAQs on Natural Free Oscillation Period

What is the formula to find Natural Free Oscillation Period?

The formula of Natural Free Oscillation Period is expressed as 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. Here is an example- 4.758255 = (2/sqrt([g]*1.05))*((3/35.23)^2+(2/30.62)^2)^-0.5.

How to calculate Natural Free Oscillation Period?

With 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) we can find Natural Free Oscillation Period using the formula - 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. This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Natural Free Oscillating Period of a Basin?

Here are the different ways to Calculate Natural Free Oscillating Period of a Basin-

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))

Can the Natural Free Oscillation Period be negative?

Yes, the Natural Free Oscillation Period, measured in Time can be negative.

Which unit is used to measure Natural Free Oscillation Period?

Natural Free Oscillation Period is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Natural Free Oscillation Period can be measured.

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Natural Free Oscillation Period Formula

​GoNatural Free Oscillation Period for Closed Basin Formula

​GoNatural Free Oscillation Period for Open Basin Formula

Natural Free Oscillation Period Example

Natural Free Oscillation Period Solution

Natural Free Oscillation Period Formula Elements

Other Formulas to find Natural Free Oscillating Period of a Basin

Other formulas in Free Oscillation Period category

How to Evaluate Natural Free Oscillation Period?

FAQs on Natural Free Oscillation Period

Variable Name

GoNatural Free Oscillation Period for Closed Basin Formula

GoNatural Free Oscillation Period for Open Basin Formula