How would you expect the solution for the system 2y" +8y 0,y(0)4,y'(0)-2 to compare with the solution for the system Give your answer, and then plot the two systems on the same graph. The graph should support your Problem3 Another factor to consider in investigating vibration of electronic components on circuit cards is the effect of damping. Engineering design often has some control over this as well. Consider the following ODE and the given initial values. Solve the system. Describe the result Next, suppose that the damping coefficients are modified. Besides including 0.5 it also includes 1.0, 1.5 and 2.0. *Solve for these four cases and plot the solutions on a single graph. Explain below how you would expect the solution of the system or ODE given below to look. Then check it with a graph. 2y', + 0.5y' + 8y = 0, y(0) 5, y' (0)--10 Problem 6 For shock and vibration testing various profiles need to be evaluated. These may be low frequency, or mid-range frequency vibrations depending on the specifications of the customer or the design team. Amplitude and time duration of these are also variables that engineering teams must address. Even thermal considerations can play a role as material properties are temperature sensitive. To address these needs the physical system is subjected to a forcing function. The differential equation for this model may take the following form. y" +p(t)y' + q(t)s g(t) # 0 Notice that such an ODE is non-homogeneous. As an example suppose that a circuit board is modeled as follows. What is the frequency of the function that drives the vibration? Solve the system with MATLAB. Describe the solution and graph the solution