Exam 2 Grading Method
Posted: Fri Oct 18, 2013 12:03 pm
Problem 1:
- Assuming right form form homogeneous solution, exp(r t), which is recognizing it's linear, constant coefficient: 5 points
- 5 points for the right form for homogeneous solution (because of repeated roots)
- 10 points for right form for particular solution, A t + B (not doing B is a big mistake)
- 5 points for right algebra for undetermined coefficients and assembling into right answer
- +5 For recognizing the mechanics/how the bolted frame moves
- +5 For recognizing the mechanics/how the spring & damper system moved (credit given for correct xp or differential equation if xp was never written)
- +5 For a reasonable expression of fg (not quite solving for the spring or damping components, but close). This was also the part where points were added/deducted for a correct explanation of how the system would be affected by the spring/damping system. Points were deducted for not taking into account the applied spring and damping forces against the ground.
- +5 For the correct spring component
- +5 For correctly evaluating the damping component.
- 5 points: Obtaining Lambda and getting general form of solution (real and complex)
- 10 points: Answer to (a). Showing that as t--> inf, limit goes to 0 in all cases (real and complex)
- 10 points: Answer to (b). All three cases (4 for any one case, 3 each for the other two cases)
- 5 total for getting close to correct substitution
- 10 total for getting the right x_0 equation
- 20 total for getting right x_0 solution
- 25 total for getting right x_1 equation