Consider the translational vibrations of a "small" rigid lathe along the cutting direction. A model of this system has a stiffness element k = 20 x 10^6 N/m, an inertia element m = 22.5 kg, and a damping coefficient /m. Determine the free response of this system for a 5 mm initial displacement and zero initial velocity. Plot the response and discuss it. How does the nature of the response of the system change when the damping coefficient is increased to.