The following has you derive the ode from the application. for each part make sure you type your answers in the text box using the equation editor and correct notation. rope of length l is attached to the ceiling and makes small vibrations. the displacement from the vertical at any point x is given by u(t, x). consider a point that is a distance x from the ceiling. explain why the weight of the cable below this point is given by w = pg(l x) where p is the linear density (mass per unit length) wu, use the definition of the derivative of f(x) to explain why f( + ax) - f(x) = ax(wuz) b. given that the restoring force can be approximated by f(x) axpg|(l- x)ug], c. next, use newton's law and the above results to explain whyparu d. finally assume u(t, x)=y(x) cos (wt + 5) and substitute this into the above formula to derive the ode (l x)y'' -y' + y=0