practice_exam3 - x = 0 where 4 represents the spring...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 2700, Fall 2011, Practice Sheet for Exam 3 Find general analytic solutions to the following differential equations. . 1. y 00 - 3 y 0 + 2 y = 0 2. y 00 + y 0 + y = 0 3. y 00 + 2 y 0 - 15 y = 0 4. y 00 + 4 y = 0 5. y 00 - 4 y = 0 6. d~v dt = A~v , where A = ± 0 1 - 2 3 ² Solve the following initial value problems (use your work above!) 7. y 00 - 4 y = 0 ,y (0) = 1 ,y 0 (0) = 3 8. y 00 + y 0 + y = 0 ,y (0) = 4 ,y 0 (0) = 0 9. d~v dt = A~v, ~v = ± 2 1 ² , where A = ± 0 1 - 2 3 ² Determine whether the fixed point at the origin is a sink, souce, node, spiral sink, or spiral source for the following systems: 10. d~v dt = A~v , where A = ± 3 1 2 3 ² 11. d~v dt = A~v , where A = ± 0 - 1 2 - 1 ² Modeling/Applications with the harmonic oscillator: 12. Suppose we have a mass on a spring described by the differential equation x 00 + dx 0 + 4
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x = 0 where 4 represents the spring constant and d the damping coecient (a positive number). For which values of d is the system undamped, underdamped, or overdamped? 13. Suppose we have a mass on a spring described by the dierential equation x 00 + 4 x = 0 (1) Find the natural resonant frequency of this oscillator. Call this . (2) Find any specic solution to the forced oscillator equation x 00 + 4 x = cos( t ) (3) Solve for, using the same , any specic solution to the forced and damped equation x 00 + 2 x + 4 x = cos( t ) 1...
View Full Document

This note was uploaded on 12/10/2011 for the course MATH 2700 taught by Professor Staff during the Fall '08 term at University of Georgia Athens.

Ask a homework question - tutors are online