{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midterm2

# midterm2 - Math 415 Midterm 2 Review Ch3.4-3.9 1...

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

Math 415 Midterm 2 Review Ch3.4-3.9 1. Homogeneous equation : ay 00 + by 0 + cy = 0 The form of the general solution depends on the solution of the characteristic eqn ar 2 + br + c = 0. (1) two real roots r 1 , r 2 : y = c 1 e r 1 t + c 2 e r 2 t (2) one real root r : y = c 1 e rt + c 2 te rt (3) complex roots λ ± : y = c 1 e λt cos μt + c 2 e λt sin μt ex) 3.4.11, 3.5.11 2.Reduction of order. Find y 2 when y 00 + py 0 + qy = 0 and a solution y 1 are given. Set y 2 = vy 1 . Look at the eqns (27)- (30) on p.171. Note that (30) is actually 1st order equation and usually this will be separable eqn. ex)3.5.25 3. Non-homogeneous equation : ay 00 + by 0 + cy = g ( t ) (1) general solution y = y h + Y (2) Method of undetermined coefficients : From g ( t ), guess the possible form of Y . (i)Consider the sum of terms of all possible derivative of g with undetermined coefficients. (ii)If this contains some homogeneous solution, multiply t or t 2 . (iii)Then plug into the equation, find the value of coefficients. ex) 3.6.13 , 3.6.19 4.Mechanical vibrations : mu 00 + γu 0 + ku = F ( t ) (1) Hooke’s law mg = kL (2) A cos w 0 t + B sin w 0 t = R cos( w o t - δ ) (p.196) (3) Check following concept (i)frequency, period, amplitude for harmonic oscillation (free undamped) (ii)quasi-frequency, quasi-period for free oscillation with underdamping

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern