5. Time shift theorem If a time function is delayed by a time a in the time domain, the result in the frequency domain is a multiplication bye Iff(t)+ F(s)we have Lf(t-a)u(t-a=e-as F(s)(a20) Example 1: Iff(0)=(a)5() (b)5u(t-5) (c)5u(t+5). Find F(s Solution (a)F(s)=5/;(b)F(s=(5S)es e 5 (c)F(s)=。5n(t+5)edt 5 e-s=5 s|05. Time shift theorem If a time function is delayed by a time in the time domain, the result in the frequency domain is a multiplication by . If we have s e − f (t)  F(s)   ( − ) ( − )= ( ) (  0) −     L f t u t e F s s Example 1: If f (t) = (a) 5u(t) (b) 5u(t-5) (c) 5u(t+5). Find F(s) Solution: (a) F(s)=5/s; (b) F(s)=(5/s)e-5s ; s s e e dt st st 5 0 5 5 0 =  − = = −  − dt  c F s u t e st   − = + 0 ( ) ( ) 5 ( 5)