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Undamped Natural Period of Vessel Formula

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Undamped Natural Period of a Vessel refers to the inherent oscillation period of a structure, such as a ship or offshore platform, in response to external forces, without considering damping effects. Check FAQs

T n = 2 \cdot π \cdot (\sqrt{\frac{m v}{k tot}})

T_n - Undamped Natural Period of a Vessel?m_v - Virtual Mass of the Ship?k_tot - Effective Spring Constant?π - Archimedes' constant?

Undamped Natural Period of Vessel Example

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Here is how the Undamped Natural Period of Vessel equation looks like with Values.

Here is how the Undamped Natural Period of Vessel equation looks like with Units.

Here is how the Undamped Natural Period of Vessel equation looks like.

0.1745 = 2 \cdot 3.1416 \cdot (\sqrt{\frac{100}{10}})

0.1745h = 2 \cdot 3.1416 \cdot (\sqrt{\frac{100kN}{10N/m}})

0.1745 = 2 \cdot 3.1416 \cdot (\sqrt{\frac{100}{10}})

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Undamped Natural Period of Vessel Solution

Follow our step by step solution on how to calculate Undamped Natural Period of Vessel?

FIRST Step Consider the formula

T n = 2 \cdot π \cdot (\sqrt{\frac{m v}{k tot}})

Next Step Substitute values of Variables

∴

T n = 2 \cdot π \cdot (\sqrt{\frac{100kN}{10N/m}})

Next Step Substitute values of Constants

∴

T n = 2 \cdot 3.1416 \cdot (\sqrt{\frac{100kN}{10N/m}})

Next Step Convert Units

∴

T n = 2 \cdot 3.1416 \cdot (\sqrt{\frac{100000N}{10N/m}})

Next Step Prepare to Evaluate

∴

T n = 2 \cdot 3.1416 \cdot (\sqrt{\frac{100000}{10}})

Next Step Evaluate

∴

T n = 628.318530717959s

Next Step Convert to Output's Unit

∴

T n = 0.174532925199433h

LAST Step Rounding Answer

∴

T n = 0.1745h

Undamped Natural Period of Vessel Formula Elements

Variables

Constants

Functions

Undamped Natural Period of a Vessel

Undamped Natural Period of a Vessel refers to the inherent oscillation period of a structure, such as a ship or offshore platform, in response to external forces, without considering damping effects.

Symbol: T_n

Measurement: TimeUnit: h

Note: Value can be positive or negative.

Formulas to find Undamped Natural Period of a Vessel

Virtual Mass of the Ship

Virtual Mass of the Ship/ Vessel is measured as the summation of mass of the vessel and mass of the vessel due to inertial effects.

Symbol: m_v

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Virtual Mass of the Ship

Effective Spring Constant

Effective Spring Constant refers to the measure of resistance provided by a structure or system to deformation due to external forces, such as waves, currents, or tides.

Symbol: k_tot

Measurement: Surface TensionUnit: N/m

Note: Value can be positive or negative.

Formulas to find Effective Spring Constant

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 Important Formulas of Mooring Forces category

Go Virtual Mass of Vessel

m v = m + m a

Go Mass of Vessel given Virtual Mass of Vessel

m = m v - m a

Go Individual Stiffness of Mooring Line

k n' = \frac{T n'}{Δl η'}

Go Elongation in Mooring Line given Individual Stiffness of Mooring Line

Δl n = \frac{T n'}{k n}

How to Evaluate Undamped Natural Period of Vessel?

Undamped Natural Period of Vessel evaluator uses Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)) to evaluate the Undamped Natural Period of a Vessel, Undamped Natural Period of Vessel is defined for undamped natural period whereas motion of ship in surge is assumed to be independent of other directions of motion. Damping is assumed to be small for low-frequency motions of ship in surge. Undamped Natural Period of a Vessel is denoted by T_n symbol.

How to evaluate Undamped Natural Period of Vessel using this online evaluator? To use this online evaluator for Undamped Natural Period of Vessel, enter Virtual Mass of the Ship (m_v) & Effective Spring Constant (k_tot) and hit the calculate button.

FAQs on Undamped Natural Period of Vessel

What is the formula to find Undamped Natural Period of Vessel?

The formula of Undamped Natural Period of Vessel is expressed as Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)). Here is an example- 4.8E-5 = 2*pi*(sqrt(100000/10)).

How to calculate Undamped Natural Period of Vessel?

With Virtual Mass of the Ship (m_v) & Effective Spring Constant (k_tot) we can find Undamped Natural Period of Vessel using the formula - Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)). This formula also uses Archimedes' constant and Square Root Function function(s).

Can the Undamped Natural Period of Vessel be negative?

Yes, the Undamped Natural Period of Vessel, measured in Time can be negative.

Which unit is used to measure Undamped Natural Period of Vessel?

Undamped Natural Period of Vessel is usually measured using the Hour[h] for Time. Second[h], Millisecond[h], Microsecond[h] are the few other units in which Undamped Natural Period of Vessel can be measured.

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Undamped Natural Period of Vessel Formula

Undamped Natural Period of Vessel Example

Undamped Natural Period of Vessel Solution

Undamped Natural Period of Vessel Formula Elements

Other formulas in Important Formulas of Mooring Forces category

How to Evaluate Undamped Natural Period of Vessel?

FAQs on Undamped Natural Period of Vessel

Variable Name