1 Signals and Systems Fall 2014 Solution to Homework Assignment #1 1. Find the differential equation relating y(t) and x(t) if Y(s)X(s)s22s3s24s3. 3222( )( )4( )3 ( )( )2( )s Y ss Y ssY sY ss X ss X sTaking inverse Laplace transform of the above equation leads to: ( )( )4 ( )3 ( )( )2 ( )y ty ty ty tx tx t. 2. With the given equation: tdxtxtyty0)()()(3)(Taking Laplace transform: 0( )( )(0)3( )( )X ssY syY sX ss13( )( )ssY sX ss21( )( )( )3sY sH sX sss. 3. Given differential equation y2yu, It can be rewritten as 2yyu(*) We firstly solve the equation: 20yy(**) Characteristic equation: 20kgives the root2k.
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