Problem 4: Consider the second order linear system defined by (1)+280, j(t) + 0), y(t)=0, y(0) = yo, (0) = y;,120 where (5,) are real constants. (a) Solve the system using the method developed in Problem 2. (b) Plot the solutions as functions of time using MATLAB. (e) Include a phase plane plot of y() versus y(t) parameterized by 1. (d) Investigate the solutions as functions of the parameters (5,0). The parameter is called the damping ratio. The parameter() is called the system natural frequency. Explain the interpretation of these terms based on your simulations. Give an example of a physical system described by the second order system model. Problem 4: Consider the second order linear system defined by (1)+280, j(t) + 0), y(t)=0, y(0) = yo, (0) = y;,120 where (5,) are real constants. (a) Solve the system using the method developed in Problem 2. (b) Plot the solutions as functions of time using MATLAB. (e) Include a phase plane plot of y() versus y(t) parameterized by 1. (d) Investigate the solutions as functions of the parameters (5,0). The parameter is called the damping ratio. The parameter() is called the system natural frequency. Explain the interpretation of these terms based on your simulations. Give an example of a physical system described by the second order system model