MATLAB CODE : Consider you have a simple mass (m= 2 kg) and spring (k=200 N/m) system and also assume you have an adjustable damper that you can change the damping ratio on it. You add this adjustable damper to you mass-spring system and apply an initial disturbance to initialize the motion. initial pos = 0.05m, initial vel = 2 m/s

1. a) Find the critical damping ratio of this system (whats the unit of it?)

2. b) Plot the motion of the mass for damping coefficients of 0, half of critical damping

   coefficient, equal to critical damping coefficient, and twice of critical damping

   coefficient. Have all four plots on the same frame. Use colored plots.

3. c) Plot the Phase-plane (state-space) for the above four cases on the same plot.

4. d) Since you have an adjustable damper, go ahead and start changing the damping

   coefficient of your damper from zero to a large number (e.g., damping ratio varies from 0 to infinity). Plot how the roots of your characteristic equation move around on your complex plane as the damping ratio changes from 0 to a large number (infinity) .

5. e) Interpret the plots of items (a), (b), and (c).