MAE_305_Midterm_2_solution_key

MAE_305_Midterm_2_solution_key - MAE 305 Ordinary...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
MAE 305 Ordinary Differential Equations, Fall 2005 Midterm Exam #2 rt e x ξ r r = ( ) 0 = r t t I r A ) sin( 1 ) ( 2 at a a t t h = () 2 2 2 2 2 2 2 1 1 ) ( a s a a as a s s a s H + = + = (a) () ( ) 2 12 / 1 1 3 / 1 2 4 / 1 2 1 1 2 1 ) ( + + + = + + = s s s s s s s Y 2 1 ) ( 2 ) ( ) ( 2 + = s s Y s sY s Y s (b) t t t e e e t y 2 2 12 1 3 1 4 1 ) ( + =
Background image of page 1

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

View Full DocumentRight Arrow Icon
MAE 305 Ordinary Differential Equations, Fall 2005 PROPER/IMPROPER NODE or SPIRAL POINT (ASYMPT. STABLE) SADDLE POINT ( UNSTABLE ) CENTER or SPIRAL POINT (STABILITY INDETERMINATE) (b) PROPER NODE SPIRAL POINT IMPROPER NODE
Background image of page 2
MAE 305 Ordinary Differential Equations, Fall 2005
Background image of page 3

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

View Full DocumentRight Arrow Icon
MAE 305 Ordinary Differential Equations, Fall 2005 0 ' ' ' 0 ' ' = + + = + T T L T X X λ π = + = T T L T T X X ' ' ' ' ' (a) ) ( ) ( ) , ( t T x X t x u = 2 2 2 L n n = L x n x X n sin ) ( = (b) 0 ) ( ) 0 ( = = L X X n=1,2,3,4,5… Note that T n ’(0)=0 + = 1 4 2 sin 1 4 2 cos 1 4 2 exp 2 2 2 n L t n L t n L t T n 0 ' ' ' 2 2 2 = + + n n n T L n T L T + = 1 4 2 sin 1 4 2 cos 1 4 2 exp sin ) , ( 2 2 2 n L t n L t n L t L x n t x u n = + = 1 2 2
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/17/2008 for the course MAE 305 taught by Professor Luigimartinelli during the Spring '06 term at Princeton.

Page1 / 5

MAE_305_Midterm_2_solution_key - MAE 305 Ordinary...

This preview shows document pages 1 - 5. Sign up to view the full document.

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