4. Problem: Consider the following scenario: A 0.5 lb. weight is attached to a hanging spring and
allowed to come to rest at equilibrium. At equilibrium, the spring is stretched 10 in past its natural
length. A dashpot supplies a damping force with damping coefficient 0.1 lb-sec/ft. The mass is
displaced 2 in above equilibrium and released from rest. Using up as the positive direction, write
(but do not solve) an initial value problem whose solution is the displacement of the mass from
equilibrium after t seconds and determine whether the system is underdamped, critically damped,
or overdamped.
Fictoinal Student's Work:
0.5
m =
0.016, mg = 0.5,s = 10 ink=-
mg
32
S
0.5
10
-= 0.05, c = 0.1 0.016y" +0.1y' +0.05y = 0
Initial conditions: y(0) = 2 in; y'(0) = 0 ⇒ y(0) = 2, y'(0) = 0
c²-4mk = 0.12-4(0.05)(0.016) ≈ 0.003 > 0 so the system is overdamped
a) Multiple parts of the student's answers are incorrect due to a repeated error. What was that one
error?
b) Correct the error and rework and parts of the problem impacted by the error. (This is probably
way more space than you need!)
