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Period for Fundamental Mode 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{4 \cdot L ba}{\sqrt{[g] \cdot d}}

T_n - Natural Free Oscillating Period of a Basin?L_ba - Length of Basin along Axis?d - Water Depth at Harbor?[g] - Gravitational acceleration on Earth?

Period for Fundamental Mode Example

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Here is how the Period for Fundamental Mode equation looks like with Values.

Here is how the Period for Fundamental Mode equation looks like with Units.

Here is how the Period for Fundamental Mode equation looks like.

5.4972 = \frac{4 \cdot 4.41}{\sqrt{9.8066 \cdot 1.05}}

5.4972s = \frac{4 \cdot 4.41m}{\sqrt{9.8066m/s² \cdot 1.05m}}

5.4972 = \frac{4 \cdot 4.41}{\sqrt{9.8066 \cdot 1.05}}

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Period for Fundamental Mode Solution

Follow our step by step solution on how to calculate Period for Fundamental Mode?

FIRST Step Consider the formula

T n = \frac{4 \cdot L ba}{\sqrt{[g] \cdot d}}

Next Step Substitute values of Variables

∴

T n = \frac{4 \cdot 4.41m}{\sqrt{[g] \cdot 1.05m}}

Next Step Substitute values of Constants

∴

T n = \frac{4 \cdot 4.41m}{\sqrt{9.8066m/s² \cdot 1.05m}}

Next Step Prepare to Evaluate

∴

T n = \frac{4 \cdot 4.41}{\sqrt{9.8066 \cdot 1.05}}

Next Step Evaluate

∴

T n = 5.49722601998895s

LAST Step Rounding Answer

∴

T n = 5.4972s

Period for Fundamental Mode 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

Length of Basin along Axis

Length of Basin along Axis refers to the distance from one end of the basin to the other, typically measured along the longest axis.

Symbol: L_ba

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Basin along Axis

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

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 in Harbor Oscillations category

Go Maximum Oscillation Period corresponding to Fundamental Mode

T 1 = 2 \cdot \frac{L ba}{\sqrt{[g] \cdot D}}

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

L ba = T 1 \cdot \frac{\sqrt{[g] \cdot D}}{2}

Go Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

d = \frac{{(2 \cdot \frac{L ba}{T n})}^{2}}{[g]}

Go Basin Length along Axis for given Period of Fundamental Mode

L ba = T n \cdot \frac{\sqrt{[g] \cdot d}}{4}

How to Evaluate Period for Fundamental Mode?

Period for Fundamental Mode evaluator uses Natural Free Oscillating Period of a Basin = (4*Length of Basin along Axis)/sqrt([g]*Water Depth at Harbor) to evaluate the Natural Free Oscillating Period of a Basin, The Period for Fundamental Mode formula is defined as the natural period of oscillation for the primary or lowest frequency mode of a system, such as a body of water or a coastal structure. This concept is significant because it helps engineers understand how the system will respond to various forces, such as waves, tides, and other environmental factors. Natural Free Oscillating Period of a Basin is denoted by T_n symbol.

How to evaluate Period for Fundamental Mode using this online evaluator? To use this online evaluator for Period for Fundamental Mode, enter Length of Basin along Axis (L_ba) & Water Depth at Harbor (d) and hit the calculate button.

FAQs on Period for Fundamental Mode

What is the formula to find Period for Fundamental Mode?

The formula of Period for Fundamental Mode is expressed as Natural Free Oscillating Period of a Basin = (4*Length of Basin along Axis)/sqrt([g]*Water Depth at Harbor). Here is an example- 37.3961 = (4*4.41)/sqrt([g]*1.05).

How to calculate Period for Fundamental Mode?

With Length of Basin along Axis (L_ba) & Water Depth at Harbor (d) we can find Period for Fundamental Mode using the formula - Natural Free Oscillating Period of a Basin = (4*Length of Basin along Axis)/sqrt([g]*Water Depth at Harbor). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

Can the Period for Fundamental Mode be negative?

Yes, the Period for Fundamental Mode, measured in Time can be negative.

Which unit is used to measure Period for Fundamental Mode?

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

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