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Time Period of Oscillation of Ship Formula

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Time Period of Oscillation of Floating Body is the time taken by the floating body to complete an oscillation about its axis. Check FAQs

T = (2 \cdot π) \cdot (\sqrt{\frac{{k G}^{2}}{GM \cdot [g]}})

T - Time Period of Oscillation of Floating Body?k_G - Radius of Gyration of Floating Body?GM - Metacentric Height of Floating Body?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Time Period of Oscillation of Ship Example

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Here is how the Time Period of Oscillation of Ship equation looks like with Values.

Here is how the Time Period of Oscillation of Ship equation looks like with Units.

Here is how the Time Period of Oscillation of Ship equation looks like.

19.1849 = (2 \cdot 3.1416) \cdot (\sqrt{\frac{8^{2}}{0.7 \cdot 9.8066}})

19.1849s = (2 \cdot 3.1416) \cdot (\sqrt{\frac{{8m}^{2}}{0.7m \cdot 9.8066m/s²}})

19.1849 = (2 \cdot 3.1416) \cdot (\sqrt{\frac{8^{2}}{0.7 \cdot 9.8066}})

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Time Period of Oscillation of Ship Solution

Follow our step by step solution on how to calculate Time Period of Oscillation of Ship?

FIRST Step Consider the formula

T = (2 \cdot π) \cdot (\sqrt{\frac{{k G}^{2}}{GM \cdot [g]}})

Next Step Substitute values of Variables

∴

T = (2 \cdot π) \cdot (\sqrt{\frac{{8m}^{2}}{0.7m \cdot [g]}})

Next Step Substitute values of Constants

∴

T = (2 \cdot 3.1416) \cdot (\sqrt{\frac{{8m}^{2}}{0.7m \cdot 9.8066m/s²}})

Next Step Prepare to Evaluate

∴

T = (2 \cdot 3.1416) \cdot (\sqrt{\frac{8^{2}}{0.7 \cdot 9.8066}})

Next Step Evaluate

∴

T = 19.1849423082944s

LAST Step Rounding Answer

∴

T = 19.1849s

Time Period of Oscillation of Ship Formula Elements

Variables

Constants

Functions

Time Period of Oscillation of Floating Body

Time Period of Oscillation of Floating Body is the time taken by the floating body to complete an oscillation about its axis.

Symbol: T

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period of Oscillation of Floating Body

Radius of Gyration of Floating Body

Radius of Gyration of Floating Body is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass about vertical axis.

Symbol: k_G

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Gyration of Floating Body

Metacentric Height of Floating Body

The Metacentric Height of Floating Body is defined as the vertical distance between the center of gravity of a body and the metacenter of that body.

Symbol: GM

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Metacentric Height of Floating Body

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

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 Buoyancy category

Go Archimedes Principle

A bouy = ρ \cdot g \cdot v

Go Buoyant Force

F buoy = p \cdot A

Go Volume of fluid displaced

V = \frac{W}{ρ df}

Go Centre of Buoyancy

B c = \frac{d}{2}

How to Evaluate Time Period of Oscillation of Ship?

Time Period of Oscillation of Ship evaluator uses Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g]))) to evaluate the Time Period of Oscillation of Floating Body, The Time Period of Oscillation of Ship is defined as the time taken by the floating body to complete an oscillation about its axis, considered when the overturning couple is suddenly removed and then the body will start oscillating. Thus, the body will be in a state of oscillation as if suspended at the meta-center. Time Period of Oscillation of Floating Body is denoted by T symbol.

How to evaluate Time Period of Oscillation of Ship using this online evaluator? To use this online evaluator for Time Period of Oscillation of Ship, enter Radius of Gyration of Floating Body (k_G) & Metacentric Height of Floating Body (GM) and hit the calculate button.

FAQs on Time Period of Oscillation of Ship

What is the formula to find Time Period of Oscillation of Ship?

The formula of Time Period of Oscillation of Ship is expressed as Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g]))). Here is an example- 19.18494 = (2*pi)*(sqrt((8^2)/(0.7*[g]))).

How to calculate Time Period of Oscillation of Ship?

With Radius of Gyration of Floating Body (k_G) & Metacentric Height of Floating Body (GM) we can find Time Period of Oscillation of Ship using the formula - Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g]))). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Square Root (sqrt) function(s).

Can the Time Period of Oscillation of Ship be negative?

No, the Time Period of Oscillation of Ship, measured in Time cannot be negative.

Which unit is used to measure Time Period of Oscillation of Ship?

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

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