5 points for the correct setup-up, i.e., right mechanics and differential equation, then either solving it or finding something equivalent from the book
1 point for each of the remaining parts if the answer is correct (even with wrong analysis)
3 points for each of the remaining parts if both the answer is correct and it is supported by analysis.
Problem 2:
5 points for the right mechanics for the springs
10 points for finding correct equivalent spring
5 points for correct analysis if one of the spring constants is doubled.
Problem 3:
2.5 points for each match.
Problem 4:
Correct method: right mechanics and solving differential equation: 10 points
Getting the right expression for M: 5 points
Correct plot: 5 points (one point each for each extreme, one point for resonance, one point for right effect of damping ratio and one free point if any of the other stuff was right)
Problem 5:
5 points for correct homogeneous solutions
13 points for using a correct method, either VoP or undetermined coefficients recognizing you had to multiply by t