Page 304 - statbility for masters and mates

292 Ship stability
where
W the ship's weight, and
g the acceleration due to gravity.
; I Wg K 2
When a ship is inclined to a small angle (y) the righting moment is given
by: where
But
Righting moment W GZ W the ship's Weight, and
GZ the righting lever.
GZ GMEsin y
; Righting moment W GM sin y
And since y is a small angle, then:
Righting moment W GM y
or
The angular acceleration d2 y dt2
; I d2 y W GZ dt2
W EK2 d2 y W GM y g dt2
W EK2 d2 y W GM y 0 g dt2
d2 y gEGMEy 0 dt2 K2
This is the equation for a simple harmonic motion having a period `T' given by the equation:
or
2p
T p
Coeff. of y
2pK 2gp K 2K
T p p p p approx.
GM GM
gEGM g