 Recent questions in Laplace transform
2022-01-20

2022-01-14

f(t)=sin(2t)-t cos(t) Jessie Lee 2021-12-19 Answered

2021-12-16

2021-12-16

Hello, i'm here because i didn't found anything general on this topic, i need to know what is the expression of the laplace transform a composed function like that : $$L\left \{ f(x)\circ g(x) \right \} = L\left \{ f(g(x)) \right \} = ??$$ my complete equation to transform is : $$\\ x(t)=4\times [\ddot{a}(t)cos(a(t))-\dot{a}(t)^2sin(a(t))] + 2500 \\ y(t)=4\times [-\ddot{a}(t)sin(a(t))-\dot{a}(t)^2cos(a(t))] + \frac{3.711}{4}\times t^2 + 2700$$ the goal is to isolate the $$a(t)$$ function as a function of $$x(t)$$ and $$y(x)$$ Thanks for your time, Robin Luiz Deragz 2021-12-11 Answered

Using the Laplace Transform Table in the textbook and Laplace Transform Properties,find the (unilateral) Laplace Transforms of the following functions: $$\displaystyle{t}{\cos{{\left(\omega_{{0}}{t}\right)}}}{u}{\left({t}\right)}$$ Marla Payton 2021-12-11 Answered

Evaluate this laplace transform of $$\displaystyle{\frac{{{1}-{e}^{{-{t}}}}}{{{t}}}}$$ and the integral exists according to wolfram Stacie Worsley 2021-12-11 Answered

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 Patricia Crane 2021-12-11 Answered

Find the Laplace transform of $$\displaystyle{f{{\left({t}\right)}}}={10}{e}^{{-{200}{t}}}{u}{\left({t}\right)}$$ Would it be correct to take out the 10 because it is a constant, find the Laplace transform of $$\displaystyle{e}^{{-{200}{t}}}$$ and then multiply it by the Laplace transform of u(t) to obtain a final answer of $$\displaystyle{10}{\left({\frac{{{1}}}{{{s}+{200}}}}\right)}{\left({\frac{{{1}}}{{{s}}}}\right)}$$ The u(t) is what is really confusing me in this problem. Deragz 2021-12-10 Answered

I have a Laplace Transform problem which I'm having trouble with: $$\displaystyle{L}{\left\lbrace{t}{\sin{{h}}}{\left({4}{t}\right)}\right\rbrace}=?$$ Jean Blumer 2021-12-09 Answered

Using the Laplace Transform Table in the textbook and Laplace Transform Properties,find the (unilateral) Laplace Transforms of the following functions: $$\displaystyle{u}{\left({t}\right)}-{u}{\left({t}-{1}\right)}$$ Marla Payton 2021-12-08 Answered

How to find the Laplace transform of $$\displaystyle{\frac{{{1}-{\cos{{\left({t}\right)}}}}}{{{t}^{{2}}}}}$$? F(S)=? diferira7c 2021-12-08 Answered

Show that $$\displaystyle{\int_{{0}}^{{\infty}}}{\frac{{{\sin{{\left({t}\right)}}}}}{{{t}}}}{\left.{d}{t}\right.}={\frac{{\pi}}{{{2}}}}$$ by using Laplace Transform method. I know that $$\displaystyle{L}{\left\lbrace{\sin{{\left({t}\right)}}}\right\rbrace}={\int_{{0}}^{{\infty}}}{e}^{{-{s}{t}}}{\sin{{\left({t}\right)}}}{\left.{d}{t}\right.}={\frac{{{1}}}{{{s}^{{2}}+{1}}}}$$ hvacwk 2021-12-08 Answered

How do I find the inverse Laplace transform of $$\displaystyle{\frac{{{4}{s}}}{{{s}^{{2}}+{4}}}}^{{2}}$$? Lucille Davidson 2021-12-08 Answered

Let $$\displaystyle\hat{{{F}}}={L}{\left({f{{\left({t}\right)}}}\right)}$$ be the Laplace transform of f(t). Show that: $$\displaystyle{L}{\left({f{{\left({a}{t}\right)}}}\right)}={\frac{{{1}}}{{{a}}}}\hat{{{F}}}{\left({\frac{{{s}}}{{{a}}}}\right)}$$ evrimesa 2021-12-07

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}:               sin(π t), 0 ≤ t <1 y''+9y= {                               y(0)=0, y′(0)=0                   0, 1 ≤ t a) Y(s)= ? (Hint: write the right hand side in terms of the Heaviside function) b) Now find the inverse transform to find y(t)= ? . (Use step(t-c) for uc(t) .) Note= π/ (s^2+π^2)(s^2+9) = π/ π^2 -9 (1/(s^2+9) - 1/(s^2+ π^2) Ronnie Baur 2021-11-23 Answered

I'd like to compute the Laplace transform of the following function: $f(t)=\begin{cases}0, & \text{if }\ 0 \le t<\pi \\ \sin(t), & \text{if }\ t \geq \pi \end{cases}$ Could someone please provide some pointers? kiki195ms 2021-11-19 Answered

The identity $$\displaystyle{\sum_{{{k}={0}}}^{{\infty}}}{a}^{{k}}{\cos{{\left({k}{x}\right)}}}={\frac{{{1}-{a}{\cos{{x}}}}}{{{1}-{2}{a}{\cos{{x}}}+{a}^{{2}}}}},{\left|{a}\right|}{<}{1}$$ can be derived by using the fact that $$\displaystyle{\sum_{{{k}={0}}}^{{\infty}}}{a}^{{k}}{\cos{{\left({k}{x}\right)}}}={R}{e}{\sum_{{{k}={0}}}^{{\infty}}}{\left({a}{e}^{{{i}{x}}}\right)}^{{k}}$$ But can it be derived without using complex variables? atodion23 2021-11-17 Answered

Determine the Laplace transforms of these functions: $$\displaystyle{a}{)}\ {f{{\left({t}\right)}}}={\left({t}-{4}\right)}{u}{\left({t}-{2}\right)}$$ $$\displaystyle{b}{)}\ {g{{\left({t}\right)}}}={2}{e}^{{-{4}{t}}}{u}{\left({t}-{1}\right)}$$ hrostentsp6 2021-11-11 Answered

Solve the initial value problem below using the method of laplace transforms. $$\displaystyle{y}{''}+{2}{y}'-{3}{y}={0},\ {y}{\left({0}\right)}={1},{y}'{\left({0}\right)}={9}$$

If you came across the necessity of Laplace transform, it is most likely that you are coming from a mechanical engineering or electrical background. The concept is used to solve differential equations, which is why it is vital to consider Laplace transform examples as you are looking through the questions and connect the dots as the equations are being approached. Remember to look through our list of answers as these will help you to address various Laplace transform problems and find solutions to complex Laplace transform questions as you are dealing with your Laplace transform equation homework.
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