Part 1 (due Friday 2/22/08 - I suggest that you make a copy of your homework before turning it in so that you can use it to study for Exam 2)
- Read through Section 3.6. Use the table on p.181 and the accompanying step-by-step instructions to help you do the problems listed below. Start the problems early! The only way to learn this material is to do lots of problems until you get the hang of it. I will discuss the method of undetermined coefficients a bit more on Wednesday, 2/20, so bring questions to class on Wednesday or to my office hours on Tuesday.
- §3.6 #1, 2, 3, 6, 15, 17, 19a, 20a, 21a, 27
Part 2 (due Wednesday 2/27/08)
- Read Section 3.9 on forced vibrations, the sooner the better. I will be discussing this material on Friday 2/22 and Monday 2/25. Even without reading the section, you now have all the tools you need to do the problems listed below. You may want to look at the discussion on p.212 to help you do Problem 1 from §3.9.
- §3.6 #9
- §3.8 #7, 17
- §3.9 #1, 5, 6, 10, 12 (For problem 1, also draw a sketch of the function.)
Homework 4 (due Friday 2/15/08)
- §3.4 #38, 39 (refer to problem 34 for an explanation of the substitution/change-of-variables method)
- §3.5 #3, 6, 11, 14, 25, 27, 31, 38, 39
- §3.8 #2, 3, 6, 11, 21, 23, 27
- Hints
- §3.8 #21: For part (a), remember that the maxima (and minima) of u(t) = R exp[-γt/2m] cos(μt - δ) occur when u'(t) = 0. Because of the exponential term, these maxima are different from the points where cos(μt - δ) = 1 (which are obviously spaced at time intervals of Td = 2π/μ ). In fact, setting u'(t) = 0 and solving for t will show that each maximum of u(t) occurs slightly before the corresponding maximum of cos(μt - δ), with the difference between the two times given by a constant time increment of (1/μ) arctan(γ/2mμ).
Homework 3 (due Friday 2/8/08)
- §3.1 #1, 5, 7, 10, 15, 17, 19, 22
- Notes on Complex Numbers (Turn in all ten problems in exercise sets I and II.)
- §3.4 #4, 8, 16, 18, 20, 31
Homework 2 (due Monday 1/28/08)
- §2.4 #1, 7, 15, 23, 25
- §2.5 #3, 5, 7, 12, 20, 22, 25
- §2.7 #1abd, 4a, 6
Homework 1 (due Wednesday 1/16/08)
- Review Problems (turn in all the problems on the first two pages, but only half of the integral problems on the last page)
- §2.1 #9, 16, 20, 32
- §2.2 #2, 3, 14, 27, 30a-e
- §2.3 #3, 5
- Hints
- §2.2 #27
- This differential equation is very similar to the logistic equation in §2.5. You will need to use integration by partial fractions in order to solve it. (See the basic formula sheet for a quick review of partial fractions.)
- For part (a), what is the domain of y(t) when y0 < 0?
- §2.2 #30: You will also need partial fractions for this problem.
- §2.3 #5: For part (c), you can estimate the amplitude graphically, or you can use the following formula:
A cos(wt) + B sin(wt) = R cos(wt - u),
where R2 = A2 + B2 and tan(u) = B/A.