Period For Fundamental Mode Calculator

Formula Used:

\[ T_n = \frac{4 \times L_{ba}}{\sqrt{[g] \times d}} \]

Natural Free Oscillating Period of a Basin (Tn):

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1. What is the Natural Free Oscillating Period?

The 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. This is a fundamental parameter in harbor and coastal engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_n = \frac{4 \times L_{ba}}{\sqrt{[g] \times d}} \]

Where:

\( T_n \) — Natural Free Oscillating Period of a Basin (seconds)
\( L_{ba} \) — Length of Basin along Axis (meters)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( d \) — Water Depth at Harbor (meters)

Explanation: The formula calculates the fundamental resonant period of a basin based on its length and water depth, using gravitational acceleration as a constant.

3. Importance of Period Calculation

Details: Accurate calculation of the natural oscillating period is crucial for harbor design, wave resonance analysis, and preventing destructive wave amplification in enclosed water bodies.

4. Using the Calculator

Tips: Enter the length of the basin along its axis and the water depth at the harbor. Both values must be positive numbers measured in meters.

5. Frequently Asked Questions (FAQ)

Q1: What factors affect the natural oscillating period?
A: The period is primarily determined by the basin length and water depth. Basin geometry and boundary conditions also play a role.

Q2: Why is gravitational acceleration used in the formula?
A: Gravitational acceleration is fundamental to wave propagation dynamics in fluids, determining the speed at which waves travel through water.

Q3: What are typical values for natural periods?
A: Natural periods can range from seconds for small basins to minutes for larger harbors, depending on their dimensions.

Q4: How does water depth affect the period?
A: Deeper water allows waves to travel faster, resulting in shorter natural periods for the same basin length.

Q5: Are there limitations to this formula?
A: This formula provides the fundamental mode period and works best for simple rectangular basins with uniform depth.