Question

4. Based on the method presented in the lesson DIFFEQ 017, provide the derivation of the Laplace transform L{sin at.

Solution steps plz

Answer 1

o Sin lat)e-st dt I- - Using Definition 2(f(+) J f (4) e-st.dt d(sincet)= si J Sin/at) e-87 at = sin(at)e-st facosat = sin lot Je-s+ + a coslat) e-stat J coste = Sin lat)e-st [cosas 'Coslat) e-87 = Sin cat)e-st a loslate-8+ sat e-st + at s ta fassinate nat e at ct 8 at al a fosinatest I = Sin (at)o-st a Coscat) est a² s s² Sin(at) est Ą a cos(at) est 32

Ó I =fsin (at) e-st det Sinlat)est 4 - a Coslat e-st lt az a la ood(sin ct) = 5 Ginlat)e-st dt = Sin (at)e-st. a alos lat)e-87 82 lt az =18² (8²ta s)[0-0 70 0-0 10 + acosloco s² [ 9 s²ta² а 8²+ a2 o 2 (osin (at)) sta²