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A ship has a radius of gyration of k=8m, a transverse metacentric height GM of 2m and a displacement force of 156960kN. If the coefficient for roll damping moment expression, b has value of 128000KNms while the ship is rolling in still water, determine the amplitude of roll after three complete oscillations if the ship was initially inclined at 5º (ie when t=0, ¢=5º and dø/dt=0)? The added mass moment of inertia is 25% of the mass moment of inertia of the ship in this case of rolling.

A ship has a radius of gyration of k=8m, a transverse metacentric height GM of 2m and a displacement force of 156960kN. If the coefficient for roll damping moment expression, b has value of 128000KNms while the ship is rolling in still water, determine the amplitude of roll after three complete oscillations if the ship was initially inclined at 5º (ie when t=0, ¢=5º and dø/dt=0)? The added mass moment of inertia is 25% of the mass moment of inertia of the ship in this case of rolling.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Problem Statement A ship has a radius of gyration of \( k_x = 8 \) m, a transverse metacentric height \( GM \) of 2 m, and a displacement force of 156960 kN. If the coefficient for roll damping moment expression \( b \) has a value of 128000 KNms while the ship is rolling in still water, determine the amplitude of roll after three complete oscillations if the ship was initially inclined at \( 5^\circ \) (i.e., when \( t = 0 \), \( \Phi = 5^\circ \) and \( d\Phi / dt = 0 \)). The added mass moment of inertia is 25% of the mass moment of inertia of the ship in this case of rolling.
Transcribed Image Text:### Problem Statement A ship has a radius of gyration of \( k_x = 8 \) m, a transverse metacentric height \( GM \) of 2 m, and a displacement force of 156960 kN. If the coefficient for roll damping moment expression \( b \) has a value of 128000 KNms while the ship is rolling in still water, determine the amplitude of roll after three complete oscillations if the ship was initially inclined at \( 5^\circ \) (i.e., when \( t = 0 \), \( \Phi = 5^\circ \) and \( d\Phi / dt = 0 \)). The added mass moment of inertia is 25% of the mass moment of inertia of the ship in this case of rolling.
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