Step function Definition and 136 Threads

I have a question that has stumped me a bit, i am not sure how to use the definition to calculate it, i can use the tables, but i don't think that's what is needed. Using the definition of the Laplace transform, determine the Laplace transform of I can do it with the table but i am not sure...

Homework Statement I'm having trouble with part b and part d, where there is some kind of ramp function involved http://img845.imageshack.us/img845/7507/76500775.jpg The Attempt at a Solution For part b, I calculated the gradient of that ramp, and the intercept which gives y = -x...

Homework Statement y'' + 4y' + 2y = u_pi(t) + u_2pi(t) y(0) = 0 and y'(0) = 0.Homework Equations the step function equation: u_c(t) = u(t-c) --> (laplace) --> e^-cs/sThe Attempt at a Solution i am having major probs with getting my head around step function probs wrt laplace transforms. What...

Homework Statement Could someone please explain this to me? I have read several notes on it, but do not really follow the reasoning: The Attempt at a Solution When t = 0, -1/s*e^-st = -1/s because e^0 = 1. When t goes to infinity is the part I do not fully understand. Why...

Write f(x) in terms of the unit step function u(x). $u(x)=\left\{ \begin{array}{rcl} 1\ &\text{if}& \ x\geq 0 \\ 0\ &\text{if}& \ x<0\end{array} \right.$ $f(x)=\left\{ \begin{array}{rcl} 1\ &\text{if}& \ 2n\le x\le 2n+1 \\ 0\ &\text{elsewhere}\end{array} \right.$

Homework Statement f(t)= 1 if 0≤t≤1 ; 0 is t>1 find the laplace transform Homework Equations The Attempt at a Solution I know u(t)= 0 for t<0 and 1 for t≥0 I know I have to shift it and get u_a(t)=u(t-a)= 1 if 0≤t≤a, 0 if a>1 am I even going the right way? then I think...

step function using MATLAB :D hey guyzzzz i got a problem with this MATLAB program ...um a beginner in using MATLAB :D...and my professor insists to solve the attached problem with MATLAB without using "if statement" and in one line command and to plot the current versus the energy...may...

Homework Statement I am trying to do some revision for an upcoming exam and one question I am trying to figure out is Use the second shifting theorem to find the Laplace transfrom of the following function: f(t) = t2, t < 4 t, t ≥ 4 Homework Equations The Attempt at a...

Homework Statement f(x) = \begin{cases} 0, & t < \pi \\ t - \pi , & \pi \leq t < 2 \pi \\ 0, & t \geq 2 \pi \end{cases} Homework Equations Unit step function: u_c(t) = \begin{cases} 0, & t < c \\ 1 , & t \geq c \\ \end{cases} The Attempt at a Solution u_{\pi}(t)(t-\pi) - u_{2...

So I'm not going to lie, I'm pretty new with this software. I was assign a homework assignment, but I'm not sure how you graph a step function. Given this waveform use the step function to find an equation: http://img163.imageshack.us/img163/2545/stepfunction.jpg" I calculated the step...

Homework Statement a particle with mass=m is in a 1-D infinite square well of width a. The particle is initially in ground state. A delta function potential V1=k δ(x-a/2) is turned on at t= -t1 and turned off at t=t1. A measurement is made at t2, where t2>t1. What is the probability that the...

Homework Statement (quick sketch of part i. yes i know the graph should specifically end at t=4 lol) Homework Equations u(t-a) = 0 for t>a = 1/2 for t=a = 1 for t>aThe Attempt at a Solution i'm having trouble solving part (ii). i remember a friend of mine saying something like "start with...

Homework Statement Hi all came across this problem whilst doing some revision and i can't work out the answer Solve the following equation with laplace transformation Homework Equations y''+16y = f(t) = { 1 t < pi ] with y(0) = 0 and y'(0) = 0 _____________{ 0 t >= pi ]...

Homework Statement L{2t u(t-1)} Homework Equations L{g(t) u(t-c)} = e^-cs L{g(t+c)} The Attempt at a Solution L{2t u(t-1)}=e^-s L{2(t+1)} L{2(t+1)}=2/s^2+2/s L{2t u(t-1)} = e^-s {2/s^2 + 2/s} i think the whole attempt is wrong , I'm getting confused in this type of...

Homework Statement [PLAIN]http://img845.imageshack.us/img845/1706/delta.png The Attempt at a Solution This question has come after a chapter on Dirac's delta-function although the question doesn't say use it. Could I use it? If not how do I do it directly?

Homework Statement f(t) = {0, if t<4 and (t-3)^3 if t\geq4 The Attempt at a Solution I feel like its pretty basic but i can't get it down I have u(t-4)(t-4)^3 Can i change it to u(t-4)^4? Then do i multiply it out and take the laplace? If someone can work it out for me that would...

Homework Statement Its not homework anyway: I'm asked to find the solution to the differential equation: i'' + 2i = f(t) i'(0)=i(0)=0 f(t) = u(t-10) - u(t-20) Unit step function (I've found in part a of the question) Then I've gotten: \mathscr{L}(i) =...

I need to know the derivative of the step function u(-t). I believe it is: -&(-t) where & represents the impulse function. Is this correct? Thanks.

Homework Statement given this discrete time signal x[n] = u[n] - u[n-6] find for which n the even part of x is 0The Attempt at a Solution the even part is x' = 1/2(x[n] + x[-n]) = 1/2(u[n] - u[n-6] + u[-n] - u[6-n]) now i find that u[n] + u[-n] is 2 for n = 0 and 1 for n != 0 u[n-6] +...

unit step function u(t) does not contain any transient signal

What is the laplace transform of a function that is 1 from 0 to 10 and 0 elsewhere? I know that this can be represented by the step function U(10-t)U(t)...but how do i find the laplace transform of this?

Homework Statement The Dirac function (unit impulse) is defined as \delta(t) = 0 where t \neq 0 the integration of d(t) between -ve inf and +ve inf is 1. Now I picture this as a rectangle with no width and infinite height. In fact I think of the width (along the x axis) as (1/inf =...

Homework Statement I need to show that the unit step function (\Theta(s) = 0 for s<0, 1 for s>0) can be written as \Theta(s)=\frac{1}{2\pi i} \int_{-\infty}^{\infty} dx \frac{e^{ixs}}{x-i0}. Homework Equations - The Attempt at a Solution Firstly, I'm unsure about what "x-i0" actually...

Homework Statement I'm trying to take the laplace transfrom of t H(t) where H(t) is the unit step function. Also, in a separate problem I get e^{-t} H(t) - e^{-t}H(t-1) and I am wondering how to manipulate it properly Homework Equations L \{ f(t-a) H(t-a) \} = e^{as}F(s) The...

Homework Statement Hello, i have a small problem regarding this questions, If the function vs(t) is a function for t>=0, i can solve thus no problem (we are required to solve using variation of parameters). now i have a small problem, its not about how to solve it ,but how to approach...

Homework Statement http://img189.imageshack.us/img189/9859/mathlm.th.jpg (Click the thumbnail)Homework Equations When taking the laplace transform of derivatives L{f^n(t)=(s^n)*F(s) - s^(n-1)*f(0)...}; the step function u(t-a) The Attempt at a Solution we have never done a step function...

Homework Statement y'+2y=f(t), y(0)=0, where f(t)=\left\{t, 0\leq t<0 \;and \; 0, t \geq 0 (I don't know how to do piecewise)Homework Equations Equation for initial conditions; step function: u(t-a) The Attempt at a Solution I know how to solve a differential equation with initial...

This is me questioning a concept, so I did not follow the template. I know that \[\int {u(t-a)dt = tu(t-a)} \] where u(t) is the unit step function. Does this mean that any arbitrary function multiplied by u(t) is just the integral of that function multiplied by u(t), and I don't have to do...

Homework Statement Find the solution to the differential equation using Laplace transforms.Homework Equations y'' - y' - 2y = 12 \theta{(t-\pi)}\sin{t} y(0) = 1 y'(0) = -1 The Attempt at a Solution Using Laplace transforms... \mathcal{L}(y'') = s^2F - s + 1 \mathcal{L}(-y') = -sF-1...

Hello, I have a question about dirac-delta function. Integral of step function from -infinity to +infinity equals to infinity from the graph of step function. \int_{-\infty}^{\infty}\theta (x) dx=\infty But calculating mathematically \lim_{a\rightarrow\infty}\int_{-a}^{a}\theta(x)...

Homework Statement I need this to answer a question, its not a homework question itself. Can this be simplified? u(t-2)u(t-a) where u is the unit step function. Homework Equations - The Attempt at a Solution I know the answer is u(t-2) if a <= 2, u(t-a) otherwise. But is there a...

what does the u(-t) mean in unit step funtion in basic function of signal and system?how can be time taken as -ve?

Homework Statement Consider the step function potential: V(x) = \{ \begin{array}{*{20}c} {0,(x \le 0)} \\ {V_0 ,(x > 0)} \\ \end{array},Caculate the reflection coefficient,for the case E<V0,and comment on the answer Homework Equations - \frac{{\hbar ^2 }}{{2m}}\frac{{d^2 \psi...

Laplace Transform of unit step function HELP! Homework Statement f(t)= e^t on 0<=t<1 . . . . t on 1<=t<2 . . . . sin(t) on 2<=t<infinity Homework Equations Unit Step Function The Attempt at a Solution Here is my attempt at a solution...

Hi, i have a problem with integration a function with a unit step function. Homework Statement Given, Refer to the image, i dun understand is that u(t) is equal to 1 from a definite integration from -\infty to \infty since u(t)=1 from -\infty to 0 and u(t)=0 from 0 to \infty...

Homework Statement The piecewise continuous function f(x) = { -8 for x ≤ 8 -x – 1 for x > 8} Rewrite it in step functions. Homework Equations The Attempt at a Solution I think it's 1-(-8)(h(x-8)) + (-x-1)(h(x-8)) Where h(x-a) is the Heaviside function (x-8) meaning it...

Homework Statement f(t)= 4t t<1 f(t)= 4 t≥1 I need to write f(t) in terms of H(t) Homework Equations H(t-t0)=0 for t<t0 = 1 for t≥t0 The Attempt at a Solution I am not too sure how it is done, as what I read online, people can just immediately...

Homework Statement u(t) * u(t) * u(t) * indicates convolution Homework Equations i know u(t) * u(t) = t u(t) The Attempt at a Solution so (t u(t)) * u(t) = \int \tau d \tau limits of integration are 0 to t so the answer is 1/2 t^2 u(t)?

if you subtract two delayed unit step functions, is the resultant a unit step function too? what is the value at the last point? 0 or 1? similarly, if you add 2 unit step functions will the magnitude of the resultant funtion be 1 or 2?

Confusion with Fourier Transform and Step Function...clarification needed please :) I am required to find the Fourier Transform of (without integration): s(t) = 1 for 0 < t < 4; -t/2 for 4 < t < 6. I understand that for: s(t) = t for 0 < t < 1; 1 for t > 1 that this is the same as...

step function - laplace... Homework Statement y"+y = f(t) f(t) = 1, t<pi/2 0, pi/2<=t<infinity The Attempt at a Solution i now have L{y} = \frac{1-e^(-(pi/2)s)+s}{s(s^2+1)} but how do i separate them and finish the problem? thanks

consider f(t)=2u(t)-2u(t-2) Volts between t=0 and t=4 seconds. So i have to find the Fourier Series Representation of this given that T=4 secounds. I am not worried about the Fourier part. If i draw the f(t) function out on graph its 2 Volts from t=0 till t=2 seconds and then wehn it gets to 2...

Homework Statement What is the Laplace transform of f(t) = 0 for 0 < t < 2 and f(t) = (4-t) for 2 < t < 3 and f(t) = 1 for 3 < t < 4 and f(t) = (5-t) for 4 < t < 5 and f(t) = 0 for t > 5? Homework Equations The Attempt at a Solution f(t) = H(t-2)(4-t) - H(t-3)(4-t) + H(t-3) - H(t-4) +...

Homework Statement plot this function: cos(pi*n)*u(n) The Attempt at a Solution n=0:1:10; y=(n>=0); x(n) = cos(pi()*n)*y figure(1) plot(y)

this isn't homework, this is just general knowledge and i can't figure it out.. please help, thx Find the Laplace transform of the given function: f(t) = { 0 t<2, (t-2)^2 t>=2 I tried working it out and this is where i get stuck f(t) = (t-2)^2 * u(t-2) I am not sure if I got the...

Hi, I currently have this problem to solve and I can't seem to figure it out it goes like this Find the Laplace transform of the given function: f(t) = { 0 t<2, (t-2)^2 t>=2 I tried working it out and this is where i get stuck f(t) = (t-2)^2 * u(t-2) I am not sure if I got...

Homework Statement Define I(x)= I( x - x_n ) = { 0 , when x < x_n { 1, when x >= x_n. Let f be the monotone function on [0,1] defined by f(x) = \sum_{n=1}^{\infty} \frac{1}{2^n} I ( x - x_n) where x_n = \frac {n}{n+1} , n \in \mathbb{N} . Find \int_0^1 f(x) dx ...

Hi Guys, I am trying to create a basic unit step function in Matlab that needs to be in the range of" -5 <= x <= 5 I need this to be done via a function and not piece together using different intervals and it needs to show the whole -5 to 5 interval. I am just beginning in Matlab and am...

Hello all. In my book (Mathematical Analysis by Apostol), the author states and proves the following theorem for real (i.e. f and alpha are functions from [a,b] to R) Riemann-Stieltjes integrals: Assume c\in(a,b) and \alpha is such that \alpha(a)=\alpha(x) when a\leq x<c, and...

Hi, Friends How to numerically do with step function? I mean, this function is very sensitive to the precision. For example, f(x) is a step function. When x is greater than some very small positive number, \delta, the numerical answer is 1, which agrees with the expected value. But when x <...