Exam II will be held in the usual room at the usual time: 11:30-12:20 on Monday Oct. 21. It will start promptly at 11:30, so make sure you're on time. The test will cover sections 3.4, 3.5, 3.6, 7.1, 7.2, 7.3, and 7.4.

The test will have four problems, possibly with several parts each. Calculators or other devices are not needed and are not to be used.

The following topics are likely to be covered, though the exam is not limited to these topics:

• mechanical vibrations: simple harmonic motion (no damping); under/over/critically damped behavior
• expressing simple harmonic motion as x(t) = C cos(ω t - α)
• mechanical systems with a simple harmonic external force; resonance (with and without damping); the natural frequency of a system; transient and steady periodic solutions
• solving non-homogeneous constant coefficient linear equations: method of undetermined coefficients to find a particular solution; choosing the correct form of that solution
• Laplace transform: definition, existence and domain of F(s), uniqueness of LT
• properties of Laplace transform: linearity, LT of derivatives and integrals, inverse LT of derivatives and integrals (of F(s)), translation in s and in t, LT of convolution f*g
• using partial fractions to compute inverse LT (including: knowing the correct form of the partial fraction decomposition)
• using LT to solve initial value problems

The subsection at the end of 3.5 called "Variation of Parameters" is not covered on this exam.

I will provide a list of Laplace transforms for you to use during the exam. Here is the list.

Advice: I recommend practicing many problems of each type, much more than the number I assigned for homework. For each type of problem you should try to reach the point where you have completely mastered it, and will be happy when you one on the exam. The only way to reach this point is by extensive practice. Remember, if you're uncomfortable now about a certain kind of problem, it may be even more difficult under the pressure of an exam situation.

When it comes time for the test itself, relax and do the best you can. Because you have studied, you know which topics you know best, and can get those problems out of the way quickly. Then you'll have plenty of time to spend on the remaining ones.