3.36 The free vibrations of a system are governed by the differential equation 2x + 40x + 1800x = 0 with initial conditions x(0) = 0.001 m and (0) = 3 m/s. Calculate or specify the following. (a) The natural frequency, (b) The damping ratio, (c) Whether the system is undamped, underdamped, critically damped, or overdamped (d) The undamped period, T (e) The frequency in Hz, f (f) The damped natural frequency (if appropriate), w (g) The logarithmic decrement (if appropriate), 6 (h) The amplitude, A (i) The phase between the response and a pure sinusoid (if appropriate), (j) The free response of the system