Time Period of One Complete Oscillations Calculator

✖The Radius of Gyration of 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.ⓘ Radius of Gyration of Body [k_G]			+10% -10%
✖Metacentric Height is the vertical distance between the center of buoyance of the body and center of gravity.where B stands for center of buoyancy and G stands for center of gravity.ⓘ Metacentric Height [GM]			+10% -10%

✖Time Period of Rolling is the time taken by a wave to complete one oscillation.ⓘ Time Period of One Complete Oscillations [T]

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Formula

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Time Period of One Complete Oscillations

Formula

`"T" = 2*pi*("k"_{"G"}^2/("[g]"*"GM"))^(1/2)`

Example

`"5.439553s"=2*pi*(("0.105m")^2/("[g]"*"0.0015m"))^(1/2)`

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Time Period of One Complete Oscillations Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Time Period of Rolling - (Measured in Second) - Time Period of Rolling is the time taken by a wave to complete one oscillation.
Radius of Gyration of Body - (Measured in Meter) - The Radius of Gyration of 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.
Metacentric Height - (Measured in Meter) - Metacentric Height is the vertical distance between the center of buoyance of the body and center of gravity.where B stands for center of buoyancy and G stands for center of gravity.

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration of Body: 0.105 Meter --> 0.105 Meter No Conversion Required
Metacentric Height: 0.0015 Meter --> 0.0015 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = 2*pi*(k_G^2/([g]*GM))^(1/2) --> 2*pi*(0.105^2/([g]*0.0015))^(1/2)

Evaluating ... ...

T = 5.43955284311121

STEP 3: Convert Result to Output's Unit

5.43955284311121 Second --> No Conversion Required

FINAL ANSWER

5.43955284311121 ≈ 5.439553 Second <-- Time Period of Rolling

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Buoyancy And Floatation » Time Period of Transverse Oscillation of a Floating Body » Time Period of One Complete Oscillations

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Created by M Naveen

National Institute of Technology (NIT), Warangal

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Verified by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< 2 Time Period of Transverse Oscillation of a Floating Body Calculators

Radius of Gyration of Body given Time Period

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

Time Period of One Complete Oscillations

Go Time Period of Rolling = 2*pi*(Radius of Gyration of Body^2/([g]*Metacentric Height))^(1/2)

Time Period of One Complete Oscillations Formula

Time Period of Rolling = 2*pi*(Radius of Gyration of Body^2/([g]*Metacentric Height))^(1/2)
T = 2*pi*(k_G^2/([g]*GM))^(1/2)

What is Radius of Gyration?

Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there.

How to Calculate Time Period of One Complete Oscillations?

Time Period of One Complete Oscillations calculator uses Time Period of Rolling = 2*pi*(Radius of Gyration of Body^2/([g]*Metacentric Height))^(1/2) to calculate the Time Period of Rolling, The Time Period of One Complete Oscillations pitching. The oscillatory motion of an object about its longitudinal axis is designated as rolling. Time Period of Rolling is denoted by T symbol.

How to calculate Time Period of One Complete Oscillations using this online calculator? To use this online calculator for Time Period of One Complete Oscillations, enter Radius of Gyration of Body (k_G) & Metacentric Height (GM) and hit the calculate button. Here is how the Time Period of One Complete Oscillations calculation can be explained with given input values -> 5.439553 = 2*pi*(0.105^2/([g]*0.0015))^(1/2).

FAQ

What is Time Period of One Complete Oscillations?

The Time Period of One Complete Oscillations pitching. The oscillatory motion of an object about its longitudinal axis is designated as rolling and is represented as T = 2*pi*(k_G^2/([g]*GM))^(1/2) or Time Period of Rolling = 2*pi*(Radius of Gyration of Body^2/([g]*Metacentric Height))^(1/2). The Radius of Gyration of 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 & Metacentric Height is the vertical distance between the center of buoyance of the body and center of gravity.where B stands for center of buoyancy and G stands for center of gravity.

How to calculate Time Period of One Complete Oscillations?

The Time Period of One Complete Oscillations pitching. The oscillatory motion of an object about its longitudinal axis is designated as rolling is calculated using Time Period of Rolling = 2*pi*(Radius of Gyration of Body^2/([g]*Metacentric Height))^(1/2). To calculate Time Period of One Complete Oscillations, you need Radius of Gyration of Body (k_G) & Metacentric Height (GM). With our tool, you need to enter the respective value for Radius of Gyration of Body & Metacentric Height 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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