Time Period of Oscillation of Ship Calculator

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Buoyancy

Forces on Submerged Bodies

✖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.ⓘ Radius of Gyration of Floating Body [k_G]			+10% -10%
✖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.ⓘ Metacentric Height of Floating Body [GM]			+10% -10%

✖Time Period of oscillation of floating body is the time taken by the floating body to complete an oscillation about its axis..ⓘ Time Period of Oscillation of Ship [T]

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Formula

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Time Period of Oscillation of Ship

Formula

`"T" = (2*pi)*(sqrt(("k"_{"G"}^2)/("GM"*"[g]")))`

Example

`"19.18494s"=(2*pi)*(sqrt((("8m")^2)/("0.7m"*"[g]")))`

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Time Period of Oscillation of Ship Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g])))
T = (2*pi)*(sqrt((k_G^2)/(GM*[g])))
This formula uses 2 Constants, 1 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
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

Time Period of Oscillation of Floating Body - (Measured in Second) - Time Period of oscillation of floating body is the time taken by the floating body to complete an oscillation about its axis..
Radius of Gyration of Floating Body - (Measured in Meter) - 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.
Metacentric Height of Floating Body - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration of Floating Body: 8 Meter --> 8 Meter No Conversion Required
Metacentric Height of Floating Body: 0.7 Meter --> 0.7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = (2*pi)*(sqrt((k_G^2)/(GM*[g]))) --> (2*pi)*(sqrt((8^2)/(0.7*[g])))

Evaluating ... ...

T = 19.1849423082944

STEP 3: Convert Result to Output's Unit

19.1849423082944 Second --> No Conversion Required

FINAL ANSWER

19.1849423082944 ≈ 19.18494 Second <-- Time Period of Oscillation of Floating Body

(Calculation completed in 00.004 seconds)

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< 11 Buoyancy Calculators

Meta-centric height in experimental method

Go Metacentric Height of Floating Body = ((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*tan(Angle of Heel)))

Angle of heel for metacentric height in experimental method

Go Angle of Heel = atan((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*Metacentric Height of Floating Body))

Movable weight for metacentric height in experimental method

Go Movable Weight on Floating Vessel = (Metacentric Height of Floating Body*Weight of Floating Vessel*tan(Angle of Heel))/(Distance Travelled by Weight on Vessel)

Time Period of Oscillation of Ship

Go Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g])))

Radius of gyration for metacentric height and time period of oscillation

Go Radius of Gyration of Floating Body = ((Time Period of Oscillation of Floating Body)*sqrt(Metacentric Height of Floating Body*[g]))/(2*pi)

Volume of body in fluid for metacentric height and BG

Go Volume of Body Submerged in Water = Moment of Inertia of Plain Floating Body/(Metacentric Height of Floating Body+Distance of CG from Center of Buoyancy)

Meta-centric height for time period of oscillation and radius of gyration

Go Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g])

Archimedes Principle

Go Archimedes Principle = Density*Acceleration Due to Gravity*Velocity

Volume of fluid displaced

Go Volume of Fluid Displaced by Body = (Weight of Displaced Fluid)/(Density of Displaced Fluid)

Centre of Buoyancy

Go Centre of Buoyancy for Floating Body = (Depth of Immersed Object in Water)/2

Buoyant Force

Go Buoyant Force = Pressure*Area

Time Period of Oscillation of Ship Formula

Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g])))
T = (2*pi)*(sqrt((k_G^2)/(GM*[g])))

What is meta-centre?

It is defined as the point about which a body starts oscillating when the body is tilted by a small angle.

What is meta-centric height?

The distance between the meta-centre of a floating body and the center of gravity of the body is called meta-centric height. It is calculated using analytical and theoretical methods.

How to Calculate Time Period of Oscillation of Ship?

Time Period of Oscillation of Ship calculator 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 calculate the Time Period of Oscillation of Floating Body, The Time Period of Oscillation of Ship is 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 calculate Time Period of Oscillation of Ship using this online calculator? To use this online calculator 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. Here is how the Time Period of Oscillation of Ship calculation can be explained with given input values -> 19.18494 = (2*pi)*(sqrt((8^2)/(0.7*[g]))).

FAQ

What is Time Period of Oscillation of Ship?

The Time Period of Oscillation of Ship is 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 and is represented as T = (2*pi)*(sqrt((k_G^2)/(GM*[g]))) or Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g]))). 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 & 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.

How to calculate Time Period of Oscillation of Ship?

The Time Period of Oscillation of Ship is 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 is calculated using Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g]))). To calculate Time Period of Oscillation of Ship, you need Radius of Gyration of Floating Body (k_G) & Metacentric Height of Floating Body (GM). With our tool, you need to enter the respective value for Radius of Gyration of Floating Body & Metacentric Height of Floating Body 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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