First using a trigonometric identity, find L{f(t)} f(t)=sin⁡2tcos⁡2t

Question

First using a trigonometric  identity, find L{f(t)}  f(t)=sin⁡2tcos⁡2t

Arham Warner · Accepted Answer

Linearity Property: suppose f1(p)andf2(p) are Laplace transformations of F1(t)andF2(t) respectively. Then:  L{c1F1(t)+c2F2(t)}=c1L{F1(t)}+c2L{F2(t)}=c1f1(p)+c2f2(p)  Also, L{sin⁡at}=ap2+a2  Given, f(t)=sin⁡2tcos⁡2t  We have to find L{f(t)} i.e. the Laplace Transformation of giveb f(t).  f(t)=sin⁡2tcos⁡2t=  =12(2sin⁡2tcos⁡2t)=  =12sin⁡4t  Taking Laplace transformation on both sides,   L{f(t)}=L{12sin⁡4t}=  =12L{sin⁡4t}=  =124p2+42=  =2p2+42  The required solution L{f(t)}=2p2+42

First using a trigonometric identity, find L{f(t)} f(t)=sin⁡2tcos⁡2t

Answered question

Answer & Explanation