Explore Laplace Transform Equations

Find Inverse laplace transform issue $\frac{2}{4 s^{2} + s}$

Izabelle Lowery 2022-10-28

Find the Laplace transform of
$\frac{\sin (t)}{t}$

Cory Russell 2022-10-27

What is the Laplace transform of $\frac{1}{1 + t}$

Ralzereep9h 2022-10-27

Show that $L {f} (s) = \frac{1}{s + 3} when f (x) = e^{- 3 x}$

faois3nh 2022-10-27

$y " + 2 y^{'} - 15 y = 6 δ (t - 9), y (0) = - 5, y^{'} (0) = 7$
Solutions to this differential equation is
$f (t) = \frac{1}{8} e^{3 t} - \frac{1}{8} e^{- 5 t}, g (t) = \frac{9}{4} e^{3 t} + \frac{11}{4} e^{- 5 t}, Y (s) = \frac{6 e^{- 9 s}}{(s + 5) (s - 3)} - \frac{5 s + 3}{(s + 5) (s - 3)}$
So, $y (t) = 6 u_{9} (t) f (t - 9) - g (t)$
Now, I want to verify initial condition y(0)=-5
So , $y (0) = \frac{6}{8} e^{- 27} - \frac{6}{8} e^{45} - \frac{9}{4} - \frac{11}{4} = - 2.62007032931 E 19 - 5$
But the initial condition is y(0)=−5, where i am wrong?

Eliza Gregory 2022-10-26

Find the Laplace transform of $f (t) = 1 + (1 - t) u_{1} (t) + (t - 2) u_{3} (t)$

rhenan5v 2022-10-26

How to Find Inverse Laplace Transform of $F (s) = \frac{1}{π} \cot^{- 1} (\frac{10 s}{π})$

Tara Mayer 2022-10-26

How to quickly compute the inverse laplace transform of $\frac{1}{(s^{2} + 1)^{2}}$

Dylan Nixon 2022-10-26

How to compute the Laplace transform $L \frac{s i n (t)}{t}$ ? I can't use the shifting theorem because of the $t^{- 1}$ ?

djo57bgfrqn 2022-10-25

How do I get the inverse laplace transform of $(s + 2) * e^{- s} / (s + 1)^{2}$

Lance Liu 2022-10-25

Laplace Transform: $\frac{1}{s^{2}} {(1 - e^{- s t_{0}})}^{2} = \frac{4}{s^{2}} e^{- s t_{0}} \sinh^{2} (\frac{1}{2} s t_{0})$
Verify for the Laplace transform of
$F (t) = {\begin{cases} t & 0 \leq t < t_{0} \\ 2 t_{0} - t & t_{0} \leq t \leq 2 t_{0} \\ 0 & t > 2 t_{0} \end{cases}$
$\begin{aligned} L {F (t)} & = \int_{0}^{t_{0}} t e^{- s t} d t + \int_{t_{0}}^{2 t_{0}} (2 t_{0} - t) e^{- s t} d t \\ = \frac{1}{s^{2}} {(1 - e^{- s t_{0}})}^{2} \\ = \frac{4}{s^{2}} e^{- s t_{0}} \sinh^{2} (\frac{1}{2} s t_{0}) \end{aligned}$
I was able to verify everything up to $\frac{1}{s^{2}} {(1 - e^{- s t_{0}})}^{2}$ , but I don't see how $\frac{1}{s^{2}} {(1 - e^{- s t_{0}})}^{2} = \frac{4}{s^{2}} e^{- s t_{0}} \sinh^{2} (\frac{1}{2} s t_{0})$ ?

Mattie Monroe 2022-10-24

Need calculate the Laplace transform of this integral $t \in [0, + \infty) \to \int_{t}^{\infty} \frac{e^{- s}}{\sqrt{s}} d s$

Kymani Hatfield 2022-10-24

I'm having a problem trying to inverse laplace transform the following equation
$h_{0} = K_{p} * \frac{1 - T s}{1 + T s} e^{- τ s}$
I've tried to solve this equation using the residue method and got the following.
$y (t) = 2 K_{p} e^{- τ s} e^{- t / T}$
$y (t) = 2 K_{p} e^{\frac{τ}{T}} e^{- t / T}$
And that is clearly wrong.

Kayla Mcdowell 2022-10-24

Calculate the inverse Laplace transform $\frac{s - 2}{(s + 1)^{4}}$

klastiesym 2022-10-24

Find the Laplace transform of the function $H (t - a) t^{n}$ . That's what I have done so far:
$L {H (t - a) t^{n}} = \int_{0}^{\infty} e^{- s t} H (t - a) t^{n} d t = \int_{a}^{\infty} e^{- s t} t^{n} d t = \int_{0}^{\infty} e^{- s (t + a)} (t + a)^{n} d t$
Could you tell me how I can continue?

Kamden Larson 2022-10-24

Laplace transform (Using tables) of following function, is this correct?
$4 H (t - 3) . t^{2}$
For my answer I used the the t-shift theorem (using tables) and I got
$4 e^{- 3 s} . \frac{2}{s^{3}}$
I have a feeling this isn't correct.

robbbiehu 2022-10-23

Integrating $e^{- x^{2}} x^{2}$
Show that $L {t^{1 / 2}} = \sqrt{π} / (2 s^{3 / 2}), s > 0$
By the definition of Laplace transform we get:
$L {t^{1 / 2}} = \int_{0}^{\infty} t^{1 / 2} e^{- s t} d t = {x = \sqrt{s t}} = \frac{2}{s^{3 / 2}} \int_{0}^{\infty} e^{- x^{2}} x^{2} d x .$

Cohen Ritter 2022-10-23

When is the Laplace variable s equal to $j ω$ ? Because I know that, by definition, $s = σ + j ω$

ormaybesaladqh 2022-10-23

How evaluate this $f (x) = x^{2} + \frac{1}{1 + 2 x^{4}}$ with fourier tranform

Antwan Perez 2022-10-23

What is the Laplace transform of $e^{3 t} \cdot \sin^{2} t$

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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