Simple step function, Laplace transform

i_am_stupid
Messages
8
Reaction score
0

Homework Statement


A system is characterized by the equation y' + 3y = r' .

When the input is r(t) = u(t) - u(t-1), find y(t) by taking the inverse Laplace transform of Y(s).

Homework Equations


The Laplace transform integral
The Laplace transform of a derivative sF(s) - f(0)

The transfer function of the system Q = s/s+3

The impulse response qimp(t) = δ(t) - 3e-3t

The Attempt at a Solution


I'm really not sure what to do here. It seems like it should be simple enough but I feel like I am not understanding the question correctly. Any hints?
 
Physics news on Phys.org
Nevermind, got it.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

What is the Inverse Laplace Transform of e^(-sx^2/2)?
Replies
10
Views
2K
Laplace transform of an ODE with a non-smooth forcing function
Replies
2
Views
2K
Mellin transform of Dirac delta function ##\delta(t-a)##
Replies
3
Views
3K
Laplace transform of the multiplication of two functions
Replies
4
Views
3K
Finding the Laplace transform of a piecewise function
Replies
3
Views
1K
A tricky inverse Laplace transform
Replies
8
Views
2K
Are these two inverse Laplace transform solutions equivalent?
Replies
2
Views
2K
Laplace transform applied to a differential equation
Replies
1
Views
1K
Solving an ODE with the Laplace transform
Replies
8
Views
2K
Partial fraction decomposition with Laplace transformation in ODE
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top