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Elberte

Answered 2021-09-24
Author has **26945** answers

asked 2021-09-13

find the Laplace transform of f (t)

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

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

asked 2021-06-06

Use the table of Laplace transform and properties to obtain the Laplace transform of the following functions. Specify which transform pair or property is used and write in the simplest form.

a) \(x(t)=\cos(3t)\)

b)\(y(t)=t \cos(3t)\)

c) \(z(t)=e^{-2t}\left[t \cos (3t)\right]\)

d) \(x(t)=3 \cos(2t)+5 \sin(8t)\)

e) \(y(t)=t^3+3t^2\)

f) \(z(t)=t^4e^{-2t}\)

a) \(x(t)=\cos(3t)\)

b)\(y(t)=t \cos(3t)\)

c) \(z(t)=e^{-2t}\left[t \cos (3t)\right]\)

d) \(x(t)=3 \cos(2t)+5 \sin(8t)\)

e) \(y(t)=t^3+3t^2\)

f) \(z(t)=t^4e^{-2t}\)

asked 2021-01-05

\(\displaystyle f{{\left({t}\right)}}={2}{u}{\left({t}-{3}\right)}{{\cos}^{2}{2}}{t}-{6}{e}^{{{2}{t}+{7}}}\delta{\left({t}+{3}\right)}\)

asked 2021-09-03

\(\displaystyle{6}{y}^{{{\left({4}\right)}}}+{7}{y}{'''}+{21}{y}\text{}{28}{y}'-{12}{y}={t}{\left({\cos{{\left({2}{t}\right)}}}+{t}{e}^{{{\frac{{-{3}{t}}}{{{2}}}}}}\right)}\)

\(y(0)=0 , y'(0)=1 , y"(0)=0 , y'''(0)=-1\)

asked 2021-12-11

I'm having trouble with the laplace transform: \(\displaystyle{L}{\left\lbrace\sqrt{{{\frac{{{t}}}{{\pi}}}}}{\cos{{\left({2}{t}\right)}}}\right\rbrace}\)

The problem gives me the transform identity \(\displaystyle{L}{\left\lbrace{\frac{{{\cos{{\left({2}{t}\right)}}}}}{{\sqrt{{\pi{t}}}}}}\right\rbrace}={\frac{{{e}^{{-{\frac{{{2}}}{{{s}}}}}}}}{{\sqrt{{s}}}}}\) but i'm not sure/confused as to why that would help me

The problem gives me the transform identity \(\displaystyle{L}{\left\lbrace{\frac{{{\cos{{\left({2}{t}\right)}}}}}{{\sqrt{{\pi{t}}}}}}\right\rbrace}={\frac{{{e}^{{-{\frac{{{2}}}{{{s}}}}}}}}{{\sqrt{{s}}}}}\) but i'm not sure/confused as to why that would help me

asked 2021-09-15

Find laplace transform of the following functions

\(\displaystyle{f{{\left({t}\right)}}}={t}{\sin{{h}}}{\left({2}{t}\right)}\)

\(\displaystyle{f{{\left({t}\right)}}}={t}{\sin{{h}}}{\left({2}{t}\right)}\)

asked 2021-09-16

Find the laplace transform of this function

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

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