A warship sailing in a seaway has the following characteristics:
LBP = 176.78 m.
B = 25.6 m.
T = 5.79 m.
Δ = 19 000 tons
KM = 7.62 m.
KG = 6.49 m.
Wave data:
Wave height Hw = 1.219 m.
Wave length Lw = 152.4 m.
Wave period Tw = 9.8 sec.

a. Find the frequency of encounter when the ship speed is 14 knots and the heading angle is 315 degrees. Compare the encountering and roll frequencies and determine whether or not the ship will roll heavily.

b. If the ship changes its heading to 325 degrees and slows down to 4 knots, would this situation be suitable to launch a missile in terms of roll motion (again, consider the encountering and roll frequencies and compare)?
Natural motion frequencies
ωheave = 0.94 rad/sec
ωpitch = 0.91 rad/sec
ωroll = 0.57 rad/sec

c. Calculate the frequency of encounter when the ship changes heading to 90 degrees (head seas) and sustains the speed of 4 knots. In this case what can you say about the motion of the ship.

d. While sailing at 90 degrees, the ship received ballast increasing the draft to T = 7.315 m. and lowering the KG to 6.187 m. and KM to 6.584 m. in order to launch a missile. How has ballasting affected the stability and roll response? (hint: think of it in terms of GM, and evaluate it as tender/stiff ship).