RAT2 - x + 10 x = 20 x (0) = 5 x (0) = 3 5 x + 20 x + 20 x...

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

View Full Document Right Arrow Icon
ME360 - Dynamic Systems Prof. Gillespie - Fall 2010 RAT 2 - Due Sept 21 due at 12:50pm Name : ................................................... For each of the following differential equations, find the characteristic roots and write them in the box. Then choose the solution from the list below. Each equation has a solution, but not all solutions match one of the equations. Hint : You will not have time to solve all of the equations or even differentiate and plug in. Use the characteristic roots and initial values to guide your choice of solution. Differential Initial Characteristic Solution equation conditions roots number ¨ x + 7
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 + 10 x = 20 x (0) = 5 x (0) = 3 5 x + 20 x + 20 x = 28 x (0) = 5 x (0) = 8 x + 3 x + 2 x = 6 x (0) = 3 x (0) = 4 x + 16 x = 144 x (0) = 5 x (0) = 12 Solutions a) x ( t ) = 1 . 4 + 3 . 6 e 2 t + 15 . 2 te 2 t b) x ( t ) = 1 . 4 + 3 . 6 e-2 t + 15 . 2 te-2 t c) x ( t ) = 4 sin 4 t + 3 cos 4 t d) x ( t ) = 9 + 3 sin4 t-4 cos4 t e) x ( t ) = 3 e-2 t + e-5 t f) x ( t ) = 2 + 6 e-2 t-3 e-5 t g) x ( t ) = 3 + 4 e-t-4 e-2 t h) x ( t ) = 5 + 4 e-t-4 e-2 t i) x ( t ) = 8 e-7 t cos 2 t + 2 e-7 t sin 2 t j) x ( t ) = 8 e-7 t cos 3 t + 2 e-7 t sin 3 t Page 1 of 1...
View Full Document

This note was uploaded on 09/28/2010 for the course MECHENG 360 taught by Professor Gillespie during the Fall '10 term at University of Michigan.

Ask a homework question - tutors are online