Question

asked 2021-09-15

Calculate the Laplace transform \(\displaystyle{L}\le{f}{t}{\left\lbrace{f}{r}{i}{g}{h}{t}\right\rbrace}\) of the function \(\displaystyle{f{{\left({t}\right)}}}={e}^{{{4}{t}+{2}}}-{8}{t}^{{6}}+{8}{\sin{{\left({2}{t}\right)}}}+{9}\) using the basic formulas and the linearity of the Laplace transform

asked 2021-09-12

Find the Laplace transform \(\displaystyle{F}{\left({s}\right)}={L}\le{f}{t}{\left\lbrace{f{{\left({t}\right)}}}{r}{i}{g}{h}{t}\right\rbrace}\) of the function \(\displaystyle{f{{\left({t}\right)}}}={2}-{7}{t}^{{5}}+{\sin{{\left({3}{t}\right)}}}\)

asked 2021-09-16

Find the laplace transform of this function

\(\displaystyle{f{{\left({t}\right)}}}={e}^{{-{2}{t}}}{\sin{{3}}}{t}{\sin{{t}}}\)

\(\displaystyle{f{{\left({t}\right)}}}={e}^{{-{2}{t}}}{\sin{{3}}}{t}{\sin{{t}}}\)

asked 2021-09-19

Derive Laplace Transform of the following:

a)\(\displaystyle{f{{\left({t}\right)}}}={e}^{{-{a}{t}}}\)

b) f(t)=t

c) \(\displaystyle{f{{\left({t}\right)}}}={t}^{{2}}\)

d) \(\displaystyle{\cos{{h}}}{t}\)

a)\(\displaystyle{f{{\left({t}\right)}}}={e}^{{-{a}{t}}}\)

b) f(t)=t

c) \(\displaystyle{f{{\left({t}\right)}}}={t}^{{2}}\)

d) \(\displaystyle{\cos{{h}}}{t}\)