Use the lineority of L and the table of Laplace transfoms to

Use the lineority of L and the table of Laplace transfoms to find.(Do not Simplify) L{3t3+ze-2t-4cos2t+sin5t}as a function of s,f(s) L{t2e3t+te-3tcos3t} as a function of 3,F(s)

Solution

a)Given:

      L{3t²+2e^-2t-4cos2t+sin5t}

    if we solve this for each term

       L{3t²}+L{2e^-2t}-L{4cos2t}+L{sin5t}

      =3.(2/s³)+2/(s-2)-[4s/(s²+4)]+5/(s²+25)

      =(6/s³)+2/(s-2)-[4s/(s²+4)]+5/(s²+25)

b)L{t²e^3t+te^-3tcos3t}

    if we solve this for each term

        L{t²e^3t}+L{te^-3tcos3t}

        = 2/(s-3)³+[1/[(s-3)s²]][s/(s²+9)]

        = 2/(s-3)³+[1/[(s-3)s]][1/(s²+9)] .