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Effective Spring Constant given Undamped Natural Period Formula

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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. Check FAQs

k tot = \frac{{(2 \cdot π)}^{2} \cdot m v}{{T n}^{2}}

k_tot - Effective Spring Constant?m_v - Virtual Mass of the Ship?T_n - Undamped Natural Period of a Vessel?π - Archimedes' constant?

Effective Spring Constant given Undamped Natural Period Example

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Here is how the Effective Spring Constant given Undamped Natural Period equation looks like with Values.

Here is how the Effective Spring Constant given Undamped Natural Period equation looks like with Units.

Here is how the Effective Spring Constant given Undamped Natural Period equation looks like.

10.5404 = \frac{{(2 \cdot 3.1416)}^{2} \cdot 100}{{0.17}^{2}}

10.5404N/m = \frac{{(2 \cdot 3.1416)}^{2} \cdot 100kN}{{0.17h}^{2}}

10.5404 = \frac{{(2 \cdot 3.1416)}^{2} \cdot 100}{{0.17}^{2}}

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Effective Spring Constant given Undamped Natural Period Solution

Follow our step by step solution on how to calculate Effective Spring Constant given Undamped Natural Period?

FIRST Step Consider the formula

k tot = \frac{{(2 \cdot π)}^{2} \cdot m v}{{T n}^{2}}

Next Step Substitute values of Variables

∴

k tot = \frac{{(2 \cdot π)}^{2} \cdot 100kN}{{0.17h}^{2}}

Next Step Substitute values of Constants

∴

k tot = \frac{{(2 \cdot 3.1416)}^{2} \cdot 100kN}{{0.17h}^{2}}

Next Step Convert Units

∴

k tot = \frac{{(2 \cdot 3.1416)}^{2} \cdot 100000N}{{612s}^{2}}

Next Step Prepare to Evaluate

∴

k tot = \frac{{(2 \cdot 3.1416)}^{2} \cdot 100000}{612^{2}}

Next Step Evaluate

∴

k tot = 10.540395148329N/m

LAST Step Rounding Answer

∴

k tot = 10.5404N/m

Effective Spring Constant given Undamped Natural Period Formula Elements

Variables

Constants

Effective Spring Constant

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.

Symbol: k_tot

Measurement: Surface TensionUnit: N/m

Note: Value can be positive or negative.

Formulas to find Effective Spring Constant

Virtual Mass of the Ship

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.

Symbol: m_v

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Virtual Mass of the Ship

Undamped Natural Period of a Vessel

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.

Symbol: T_n

Measurement: TimeUnit: h

Note: Value can be positive or negative.

Formulas to find Undamped Natural Period of a Vessel

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

Other formulas in Mooring category

Go Virtual Mass of Vessel given Undamped Natural Period

m v = \frac{{T n}^{2} \cdot k tot}{{(2 \cdot π)}^{2}}

Go Mass of Vessel due to Inertial Effects of Water entrained with Vessel

m a = m v - m

Go Percent Elongation in Mooring Line

ε m = 100 \cdot (\frac{Δl η'}{ln})

Go Length of Mooring Line given percent Elongation in Mooring Line

ln = \frac{Δl η'}{\frac{ε m}{100}}

How to Evaluate Effective Spring Constant given Undamped Natural Period?

Effective Spring Constant given Undamped Natural Period evaluator uses Effective Spring Constant = ((2*pi)^2*Virtual Mass of the Ship)/Undamped Natural Period of a Vessel^2 to evaluate the Effective Spring Constant, The Effective Spring Constant given Undamped Natural Period formula is defined as 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 is denoted by k_tot symbol.

How to evaluate Effective Spring Constant given Undamped Natural Period using this online evaluator? To use this online evaluator for Effective Spring Constant given Undamped Natural Period, enter Virtual Mass of the Ship (m_v) & Undamped Natural Period of a Vessel (T_n) and hit the calculate button.

FAQs on Effective Spring Constant given Undamped Natural Period

What is the formula to find Effective Spring Constant given Undamped Natural Period?

The formula of Effective Spring Constant given Undamped Natural Period is expressed as Effective Spring Constant = ((2*pi)^2*Virtual Mass of the Ship)/Undamped Natural Period of a Vessel^2. Here is an example- 10.5404 = ((2*pi)^2*100000)/612^2.

How to calculate Effective Spring Constant given Undamped Natural Period?

With Virtual Mass of the Ship (m_v) & Undamped Natural Period of a Vessel (T_n) we can find Effective Spring Constant given Undamped Natural Period using the formula - Effective Spring Constant = ((2*pi)^2*Virtual Mass of the Ship)/Undamped Natural Period of a Vessel^2. This formula also uses Archimedes' constant .

Can the Effective Spring Constant given Undamped Natural Period be negative?

Yes, the Effective Spring Constant given Undamped Natural Period, measured in Surface Tension can be negative.

Which unit is used to measure Effective Spring Constant given Undamped Natural Period?

Effective Spring Constant given Undamped Natural Period is usually measured using the Newton per Meter[N/m] for Surface Tension. Millinewton per Meter[N/m], Gram-Force per Centimeter[N/m], Dyne per Centimeter[N/m] are the few other units in which Effective Spring Constant given Undamped Natural Period can be measured.

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Effective Spring Constant given Undamped Natural Period Formula

Effective Spring Constant given Undamped Natural Period Example

Effective Spring Constant given Undamped Natural Period Solution

Effective Spring Constant given Undamped Natural Period Formula Elements

Other formulas in Mooring category

How to Evaluate Effective Spring Constant given Undamped Natural Period?

FAQs on Effective Spring Constant given Undamped Natural Period

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