Radius of gyration for metacentric height and time period of oscillation Calculator

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Physics	Fluid Mechanics ↺
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✖The time period of oscillations is the time taken by a complete cycle of the wave to pass a point.ⓘ Time period of oscillations [T]			+10% -10%
✖The metacentric height m is defined as the vertical distance between the center of gravity of a body and metacenter of that body.ⓘ metacentric height m [GM]			+10% -10%

✖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.ⓘ Radius of gyration for metacentric height and time period of oscillation [k_G]

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Radius of gyration for metacentric height and time period of oscillation

Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has created this Calculator and 300+ more calculators!

Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has verified this Calculator and 100+ more calculators!

< 4 Other formulas that you can solve using the same Inputs

Time response in overdamped case

Time response in overdamped case=1-(e^(-(Damping ratio-sqrt((Damping ratio^2)-1))*(Natural frequency*Time period of oscillations))/(2*sqrt((Damping ratio^2)-1)*(Damping ratio-sqrt((Damping ratio^2)-1)))) GO

Time response in critically damped case

Time response in critically damped case=1-e^(-(Natural frequency*Time period of oscillations))*(1+(Natural frequency*Time period of oscillations)) GO

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

metacentric height m=(4*(pi^2)*(Radius of gyration^2))/((Time period of oscillations^2)*9.81) GO

Time response in undamped case

Time response in undamped case=1-cos(Natural frequency*Time period of oscillations) GO

< 4 Other formulas that calculate the same Output

Radius of Gyration of Column when Elastic Critical Buckling Load is Given

Radius of gyration=(Coefficient for Column End Conditions*Length)/(pi*Young's Modulus)*(sqrt(Critical Buckling Load/Cross sectional area)) GO

Radius of Gyration When Time Period of Rolling is Given

Radius of gyration=sqrt((Acceleration Due To Gravity*Metacentric height)*((Time period of rolling/2*pi)^2)) GO

Radius of Gyration of Column when Allowable Compressive Stress for Aluminium Columns is Given

Radius of gyration=sqrt(Compressive Stress*(Length^2)/(End Fixity Coefficient*(pi^2)*Young's Modulus)) GO

Radius of gyration if moment of inertia and area is known

Radius of gyration=sqrt(Area Moment Of Inertia/Area of cross section) GO

Radius of gyration for metacentric height and time period of oscillation Formula

Radius of gyration=((Time period of oscillations^2)*metacentric height m*9.81)/(4*(pi^2))
k<sub>G</sub>=((T^2)*GM*9.81)/(4*(pi^2))

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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 Radius of gyration for metacentric height and time period of oscillation?

Radius of gyration for metacentric height and time period of oscillation calculator uses Radius of gyration=((Time period of oscillations^2)*metacentric height m*9.81)/(4*(pi^2)) to calculate the Radius of gyration, The Radius of gyration for metacentric height and time period of oscillation is given by the relation of oscillation in floating bodies in which the overturning couple is removed. Then the body starts oscillating as if suspended at the meta-centre. Radius of gyration and is denoted by k_G symbol.

How to calculate Radius of gyration for metacentric height and time period of oscillation using this online calculator? To use this online calculator for Radius of gyration for metacentric height and time period of oscillation, enter Time period of oscillations (T) and metacentric height m (GM) and hit the calculate button. Here is how the Radius of gyration for metacentric height and time period of oscillation calculation can be explained with given input values -> 8945.647 = ((60^2)*10*9.81)/(4*(pi^2)).

FAQ

What is Radius of gyration for metacentric height and time period of oscillation?

The Radius of gyration for metacentric height and time period of oscillation is given by the relation of oscillation in floating bodies in which the overturning couple is removed. Then the body starts oscillating as if suspended at the meta-centre and is represented as k_G=((T^2)*GM*9.81)/(4*(pi^2)) or Radius of gyration=((Time period of oscillations^2)*metacentric height m*9.81)/(4*(pi^2)). The time period of oscillations is the time taken by a complete cycle of the wave to pass a point and The metacentric height m is defined as the vertical distance between the center of gravity of a body and metacenter of that body.

How to calculate Radius of gyration for metacentric height and time period of oscillation?

The Radius of gyration for metacentric height and time period of oscillation is given by the relation of oscillation in floating bodies in which the overturning couple is removed. Then the body starts oscillating as if suspended at the meta-centre is calculated using Radius of gyration=((Time period of oscillations^2)*metacentric height m*9.81)/(4*(pi^2)). To calculate Radius of gyration for metacentric height and time period of oscillation, you need Time period of oscillations (T) and metacentric height m (GM). With our tool, you need to enter the respective value for Time period of oscillations and metacentric height m and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Radius of gyration?

In this formula, Radius of gyration uses Time period of oscillations and metacentric height m. We can use 4 other way(s) to calculate the same, which is/are as follows -

Radius of gyration=(Coefficient for Column End Conditions*Length)/(pi*Young's Modulus)*(sqrt(Critical Buckling Load/Cross sectional area))
Radius of gyration=sqrt(Compressive Stress*(Length^2)/(End Fixity Coefficient*(pi^2)*Young's Modulus))
Radius of gyration=sqrt((Acceleration Due To Gravity*Metacentric height)*((Time period of rolling/2*pi)^2))
Radius of gyration=sqrt(Area Moment Of Inertia/Area of cross section)

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