(Solved): Dynamic of marine vessel Let prove this equation (Free, Undamped Heaving Motion) to solution and giv ...

Let prove this equation (Free, Undamped Heaving Motion) to solution and give me explanation in physics, and math! There is equation of motion when equilibrium condition, $a\ddot{z}+cz=0$ there is condition where $Fo=0,b=0$. $a\ddot{z}+cz=0$ Where: $a$ is the virtual mass (ship mass plus added mass), $\ddot{z}={\mathrm{d}}^{2}z/{\mathrm{dt}}^2$ is vertical acceleration $\mathrm{c}$ is the restoring or spring constant, $\mathrm{z}=$ is displacement of the center of gravity (CG) of the ship $?$ (Look at No.1 for detailed) and the solution of this equation is $z=A\sin {?}_{z}t+B\cos {?}_{z}t$ or $z=A\sin \left({?}_{z}t??\right)$ Where A dan B are constants that can be determined from initial condition, ${?}_z$ is the natural frequency of the heaving motion, that is, $\begin{array}{rl}{?}_z& =\frac{2?}{T}\\ & =\sqrt{\frac{c}{a}}\end{array}$