My homework question is: If the ocean surface is disturbed by a wave, η=η_0 cos(ωt-kx), show that the dispersion equation is given by ω^2=gHk^2+f^2. I have looked every where and while there is alot of sites with this on they tend to just jump from one to the other saying 'substitue and solve to get....' and dont show the steps in between. I cant find the steps in any of the recommended course books either. Could some one please help me understand how to move from one to the other? Thank you.