Laplace transforms are used to solve ordinary differential equations. Once the variable of interest is manipulated to the left side of the differential equation, Laplace transforms are taken of both sides. It then becomes easier to solve for F(s). Once this is done the inverse transform can be applied
If a math platform such as MATLAB is available, then the math package can be used to solve the differential equations. Bode and other plots can then be plotted to determine the system response