For Exam #1:
(Assume a mass m, and a spring constant k)
There once were a mass and a spring,
To each other they firmly did cling.
But one day in the lab
Walter gave them a jab
At what frequency did they to swing?
(Acceptable answers: omega-naught, Sqrt[k/m])
For Exam #2:
There once were three beads on a string,
But one of them thought it was king.
It sat in the middle
Its thumbs it did twiddle
In which normal mode did they swing?
(Answer: Mode n=2)