SolSec3_8 - 3- 68Problems and Solutions Section 3.8 (3.53...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 3- 68Problems and Solutions Section 3.8 (3.53 through 3.56) 3.53Show that a critically damped system is BIBO stable. Solution: For a critically damped system h t!"( )=1mt!"( )e!#nt!"()Let f(t) be bounded by the finite constant M. Using the inequality for integrals and Equation (3.96) yields: x t( )!f(")t#h t$"( )d"=Mt#1mt$"( )e$%nt$"()d"The function h(t– τ) decays exponentially and hence is bounded by some constant times 1/t, say M1/t. This is just a statement the exponential decays faster then “one over t” does. Thus the above expression becomes; x(t)<MM1tt!d"=MM1This is bounded, so a critically damped system is BIBO stable. 3- 693.54Show that an overdamped system is BIBO stable. Solution: For an overdamped system, h t!"( )=12m#n$2!1e!$#nt!"()e#n$2!1%&’()*t!"()!e!#n$2!1%&’()*t!"()%&’()*Let f(t) be bounded by M, From equation (3.96), x t( )!Mt"h t#$( )d$x t( )!Mt"12m%n&2#1e#&%nt#$()e%n&2#1’()*+,t#$()#e#%n&2#1’()*+,t#$()’()*+,d$x t( )!...
View Full Document

This note was uploaded on 03/31/2009 for the course MECHANICAL MAE351 taught by Professor J.g.lee during the Spring '09 term at Korea Advanced Institute of Science and Technology.

Page1 / 4

SolSec3_8 - 3- 68Problems and Solutions Section 3.8 (3.53...

This preview shows document pages 1 - 3. Sign up to view the full document.

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