{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PracticeProblemsMidterm_solu

The associated time constant is 1 033 which is larger

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

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

Unformatted text preview: tory but is enclosed by two boundaries described by ±e t . The associated time constant is 1/ = 0.33, which is larger than the time constant of A. Therefore, A has the fastest convergence. 19. Consider a second order system having a pair of complex poles at 3 ± 4j . What are the damping ratio ⇣ and undamped natural frequency !n ? Solution: The undamped natural frequency !n is the distance between the origin and the pole + p 2 + ! 2 . With numerical values j ! , that is, !n = = 3 and ! = 4, we have !n = 5 . The damping ratio is given by sin where is the angle between the imaginary axis and the line connecting the origin and the pole + j ! . Drawing the ﬁgure, complex poles at 19. Consider a second order system having a pair of we see that sin 3= 4j .!n = 3/5. Hence, ⇣ = 0.6 . ± / What are the damping ratio ⇣ and undamped natural frequency !n ? 20. Consider the step responses of the following systems: Solution: The undamped natural frequency !n is the distance between the origin and t...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online