Natural Free Oscillation Period Given Maximum Horizontal Particle Excursion At Node Calculator

Natural Free Oscillating Period Formula:

\[ T_n = \frac{2 \pi X}{H_{wave} \sqrt{\frac{g}{D_w}}} \]

Natural Free Oscillating Period (T_n):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Natural Free Oscillation Period?

Natural Free Oscillating Period of a Basin referred to as the natural period or resonant period, is the time it takes for a wave to travel from one end of the basin to the other and back again. It represents the inherent oscillation characteristics of a water body.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_n = \frac{2 \pi X}{H_{wave} \sqrt{\frac{g}{D_w}}} \]

Where:

\( T_n \) — Natural Free Oscillating Period (s)
\( X \) — Maximum Horizontal Particle Excursion (m)
\( H_{wave} \) — Wave Height (m)
\( D_w \) — Depth of Water (m)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( \pi \) — Archimedes' constant (3.141592653589793)

Explanation: This formula calculates the natural oscillation period of a water basin based on wave characteristics and water depth, considering gravitational effects.

3. Importance of Natural Period Calculation

Details: Understanding the natural oscillation period is crucial for coastal engineering, harbor design, tsunami prediction, and understanding resonance phenomena in enclosed water bodies.

4. Using the Calculator

Tips: Enter maximum horizontal particle excursion in meters, wave height in meters, and water depth in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is Maximum Horizontal Particle Excursion?
A: Maximum Horizontal Particle Excursion refers to the maximum distance that a particle can travel horizontally from its initial position under the influence of a wave or current.

Q2: How is Wave Height defined in this context?
A: Wave Height is formed when two equal waves are going in opposite direction and create the usual up/down motion of the water surface, but the waves don't progress.

Q3: What factors affect the Natural Free Oscillation Period?
A: The period is primarily influenced by basin geometry, water depth, and wave characteristics. Deeper water generally results in shorter oscillation periods.

Q4: Why is this calculation important for harbor design?
A: Knowing the natural oscillation period helps prevent resonance effects that could amplify wave action and cause damage to harbor structures.

Q5: Are there limitations to this formula?
A: This formula assumes ideal conditions and may need adjustments for complex basin geometries, varying depths, or non-linear wave effects.