An automobile weighing 3000 lb is put in motion on a level highway and then allowed to coast to rest. Its speed is measured at successive increments of time, as recorded in thefollowing table:
Time (s) Speed (f t/s, approx.)
0 15.2
10 10.1
20 6.6
30 4.5
40 2.9
50 2.1
60 1.25
a) Using a mass-damper model for this system, draw the system diagram and set up the differential equation for the velocity v1 of the vehicle.
(b) Evaluate m and then estimate b by using a graph of the data given in the preceding table. (Hint: Use the slope dv1 /dt and v1 itself at any time t.)