Answer Happy

In this problem, we are going to reanalyse a spring-mass system with some damping using the phase portrait method. The equation we consider is: me" + bx' + kr =0 (1) without driven forces. Here, we assume m.b.k > 0. (2 pt.) Then, convert the sping-mass equation (1) to a system of first-order equations for y1 = 2 and 42 = 2', and distinguish the over-damped, critically damped, and underdamped cases by writing the general solution for (91-92). For each cases, draw the phase portrait after you choose arbitrary m,b, and k satisfying conditions. (For the definition of over-damped, critically damped, and underdamped, please refer to the lecture.)