Undamped Natural Period of Vessel Calculator

✖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.ⓘ Virtual Mass of the Ship [m_v]			+10% -10%
✖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.ⓘ Effective Spring Constant [k_tot]			+10% -10%

✖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.ⓘ Undamped Natural Period of Vessel [T_n]

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Undamped Natural Period of Vessel Solution

STEP 0: Pre-Calculation Summary

Formula Used

Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant))
T_n = 2*pi*(sqrt(m_v/k_tot))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

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

Undamped Natural Period of a Vessel - (Measured in Second) - 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.
Virtual Mass of the Ship - (Measured in Newton) - 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.
Effective Spring Constant - (Measured in Newton per Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Virtual Mass of the Ship: 100 Kilonewton --> 100000 Newton (Check conversion here)
Effective Spring Constant: 10 Newton per Meter --> 10 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = 2*pi*(sqrt(m_v/k_tot)) --> 2*pi*(sqrt(100000/10))

Evaluating ... ...

T_n = 628.318530717959

STEP 3: Convert Result to Output's Unit

628.318530717959 Second -->0.174532925199433 Hour (Check conversion here)

FINAL ANSWER

0.174532925199433 ≈ 0.174533 Hour <-- Undamped Natural Period of a Vessel

(Calculation completed in 00.020 seconds)

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< Important Formulas of Mooring Forces Calculators

Undamped Natural Period of Vessel

LaTeX Go Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant))

Individual Stiffness of Mooring Line

LaTeX Go Individual Mooring Line Stiffness = Axial Tension or Load on a Mooring Line/Elongation in the Mooring Line

Mass of Vessel given Virtual Mass of Vessel

LaTeX Go Mass of a Vessel = Virtual Mass of the Ship-Mass of Vessel due to Inertial Effects

Virtual Mass of Vessel

LaTeX Go Virtual Mass of the Ship = Mass of a Vessel+Mass of Vessel due to Inertial Effects

Undamped Natural Period of Vessel Formula

LaTeX Go

Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant))
T_n = 2*pi*(sqrt(m_v/k_tot))

What is Froude law?

Froude's Law, defines that the speed attainable by a creature or a ship is proportional to the square root of its scale. Froude number (Fr), in hydrology and fluid mechanics, dimensionless quantity used to indicate the influence of gravity on fluid motion.

How to Calculate Undamped Natural Period of Vessel?

Undamped Natural Period of Vessel calculator uses Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)) to calculate 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 calculate Undamped Natural Period of Vessel using this online calculator? To use this online calculator for Undamped Natural Period of Vessel, enter Virtual Mass of the Ship (m_v) & Effective Spring Constant (k_tot) and hit the calculate button. Here is how the Undamped Natural Period of Vessel calculation can be explained with given input values -> 4.8E-5 = 2*pi*(sqrt(100000/10)).

FAQ

What is Undamped Natural Period of 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 and is represented as T_n = 2*pi*(sqrt(m_v/k_tot)) or Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)). 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 & 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.

How to calculate Undamped Natural Period of 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 is calculated using Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)). To calculate Undamped Natural Period of Vessel, you need Virtual Mass of the Ship (m_v) & Effective Spring Constant (k_tot). With our tool, you need to enter the respective value for Virtual Mass of the Ship & Effective Spring Constant 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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