ps4final

ps4final - 18.03 Problem Set 4 Due by 12:45 P.M., Friday,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Due by 12:45 P.M., Friday, March 14, 2008, in the boxes at 2-106, next to the Under- graduate Mathematics Office. I encourage collaboration on homework in this course. However, if you do your homework in a group, be sure it works to your advantage rather than against you. Good grades for homework you have not thought through will translate to poor grades on exams. You must turn in your own writeups of all problems, and, if you do collaborate, you must write on the front of your solution sheet the names of the students you worked with. Because the solutions will be available immediately after the problem sets are due, no extensions will be possible . L13 W 5 Mar Driven systems: Superposition, sinusoidal harmonic response: Notes O.1; EP 2.6, pp. 157–159 only—see SN 7 if you want to learn about beats. R9 Th 6 Mar Complex numbers and phase lag. L14 F 7 Mar Operators, exponential response formula: SN 10, Notes O.1, 2, 4, EP 2.6 (pp. 165–167). L15 M 10 Mar Undetermined coefficients; RLC circuits: SN 11, EP 2.5 (pp. 144–153); EC 2.7, SN 8. R10 T 11 Mar Operators, ERF, undetermined coefficients. L16 W 12 Mar Frequency response: SN 14. R11 Th 13 Mar Ditto. L17 F 14 Mar Linear time invariant operators. Part I. 13. (W 5 Mar) (a) [From R8.] Two facts about solutions to m ¨ x + b ˙ x + kx = 0: (i) The real part of a solution is again a solution. (ii) Any constant multiple of a solution is again a solution. So if e rt is a solution (with r = a + ci a complex root, say), then so is z 0 e rt , for any complex number z 0 . If we write z 0 = Ae - φi (so A = | z 0 | and φ = - Arg ( z 0 )), what is the real part of z 0 e rt ? Explain why this gives the general solution. What would you take for z 0 to get Im e rt ? (b) For each of the following functions f ( t ), find a complex number z 0 and a positive real number ω such that f ( t ) = Re ( z 0 e iωt ). (i) cos(2 t ). (ii) 2 sin( πt ). (iii) cos( t + π 4 ). (iv) cos( t ) + 3 sin( t ). (c)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

ps4final - 18.03 Problem Set 4 Due by 12:45 P.M., Friday,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online