Let f satisfy f (t +T) = f(t) for all t> 0 and for some fixed positive number T; f is said to be a periodic with the period T on 0

Let f satisfy f (t +T) = f(t) for all t> 0 and for some fixed positive<br>number T; f is said to be a periodic with the period T on 0 <t < ∞.<br>Then, the Laplace transform of f(t) is given by<br>1<br>L{f(t)}<br>-st<br>e<br>ot f(t) dt.<br>1– e-sT<br>0.<br>Use this fact to find the Laplace transform of the given function.<br>S1, 0<t< 4<br>10, 4<t<8<br>f(t) =<br>f(t + 8) = f(t)<br>L{f(t)} =<br>

Extracted text: Let f satisfy f (t +T) = f(t) for all t> 0 and for some fixed positive number T; f is said to be a periodic with the period T on 0 < ∞.="" then,="" the="" laplace="" transform="" of="" f(t)="" is="" given="" by="" 1="" l{f(t)}="" -st="" e="" ot="" f(t)="" dt.="" 1–="" e-st="" 0.="" use="" this="" fact="" to="" find="" the="" laplace="" transform="" of="" the="" given="" function.="" s1,=""><>< 4="" 10,=""><><8 f(t)="f(t" +="" 8)="f(t)" l{f(t)}="">

Jun 04, 2022

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Let f satisfy f (t +T) = f(t) for all t> 0 and for some fixed positive number T; f is said to be a periodic with the period T on 0

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