Using the derivative theorem and, find the Laplace transform of the following functions

$r\mathrm{cos}h\left(t\right)$

Lipossig
2021-09-13
Answered

Using the derivative theorem and, find the Laplace transform of the following functions

$r\mathrm{cos}h\left(t\right)$

You can still ask an expert for help

firmablogF

Answered 2021-09-14
Author has **92** answers

Laplase transform of $t\mathrm{cos}\left(h\right)t$

$L\left(t\mathrm{cos}\left(h\right)t\right)$

derivative of Laplase transform of$\mathrm{cos}\left(h\right)t$

$\therefore L\left(\mathrm{cos}ht\right)=\frac{s}{{s}^{2}-1}$

$\therefore L\left(t\mathrm{cos}ht\right)=\frac{d}{ds}\frac{s}{{s}^{2}-1}=\frac{{s}^{2}-1-2{s}^{2}}{{({s}^{2}-1)}^{2}}{(-1)}^{2}$

$=\frac{-{s}^{2}-1}{{({s}^{2}-1)}^{2}}(-1)$

$=\frac{{s}^{2}+1}{{({s}^{2}-1)}^{2}}$

derivative of Laplase transform of

asked 2021-02-04

Find the inverse Laplace transforms of the functions given. Accurately sketch the time functions.

a)$F(s)=\frac{3{e}^{-2s}}{s(s+3)}$

b)$F(s)=\frac{{e}^{-2s}}{s(s+1)}$

c)$F(s)=\frac{{e}^{-2s}-{e}^{-3s}}{2}$

a)

b)

c)

asked 2020-11-01

Calculate the Laplace transform

$L\{\mathrm{sin}(t-k)\cdot H(t-k)\}$

asked 2021-09-13

Find the Laplace transform of $4{t}^{2}+5{t}^{3}$

asked 2022-01-20

Solve: $\frac{dy}{dx}-\frac{dx}{dy}=\frac{y}{x}-\frac{x}{y}$

asked 2021-02-09

Solve $y(t)+2{\int}_{0}^{t}{e}^{-2(t-\tau )}y(\tau )d\tau ={e}^{-2t}$

asked 2022-03-16

What is the inverse laplace transform of $F\left(s\right)=\frac{1}{2}\mathrm{ln}\left(\frac{{s}^{{}^{\left\{2\right\}}}+{b}^{2}}{{s}^{{}^{\left\{2\right\}}}+{a}^{2}}\right)$ with $a,b\text{}\u03f5\text{}\mathbb{R}$ ?

asked 2021-10-04

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s. At what rate is his distance from second base decreasing when he is halfway to first base?