This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: sin 3 y t A B t C t = + + . Since the poles are purely imaginary, the time response is marginally stable. Time Response For the transfer function ( 29 2 20 6 144 T s s s =+ , the poles are at 3 3 15 j + and 3 3 15 j, and there are no finite zeros. Since the poles are complex, the time response is underdamped and the general time response to a step input is ( 29 ( 29 ( 29 ( 29 3 3 3 cos 3 15 sin 3 15 cos 3 15 t t t y t A Be t A Ce t De t φ = + + = + + . Since the real parts of the poles are positive, the time response is unstable. For the transfer function ( 29 ( 29 2 5 10 s T s s + = + , the poles are at –10 and –10, and there is a zero at –5. Since the poles are real and equal, the time response is critically damped and the general time response to a step input is ( 29 10 10 t t y t A Be Cte= + + . Since the real parts of the poles are negative, the time response is stable. 2...
View
Full Document
 Spring '11
 LANDERS
 Laplace, time response

Click to edit the document details