A function f (t) is given as. Find the laplace transformation of this function

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

Your answer

asked 2021-09-12

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

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 2021-09-09

First using a trigonometric

identity, find \(\displaystyle{L}{\left\lbrace{f{{\left({t}\right)}}}\right\rbrace}\)

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

identity, find \(\displaystyle{L}{\left\lbrace{f{{\left({t}\right)}}}\right\rbrace}\)

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

asked 2021-10-15

Evaluate the integrals

\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{\left[{\cos{{t}}}{i}-{\sin{{2}}}{t}{j}+{{\sin}^{{{2}}}{t}}{k}\right]}{\left.{d}{t}\right.}\)

\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{\left[{\cos{{t}}}{i}-{\sin{{2}}}{t}{j}+{{\sin}^{{{2}}}{t}}{k}\right]}{\left.{d}{t}\right.}\)

asked 2021-09-27

Let F(s) be the Laplace tranform of \(\displaystyle{f{{\left({x}\right)}}}={t}{\cos{{\left({2}{t}\right)}}}\)

find the value of F(1)

find the value of F(1)

asked 2021-09-23

find the Laplace transform of f (t).

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

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

asked 2021-09-13

find the Laplace transform of f (t)

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

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