Step function Definition and 142 Threads

Homework Statement Find laplace trasform of g(t) g(t) = 0 for 0<t<1, t^2 for t>1 So this can be re-written as g(t) = t2*u1(t), where u is the unit step function. By using the fact that L(uc(t)f(t-c)) = e-csF(s) i am trying to take the laplace... So in this case, f(t-c) = t2 ... so then does...

Homework Statement I need to solve the ODE y''-y = t - tH(t-1); y(0)=y'(0)=0 Homework Equations - The Attempt at a Solution I'm fine with the process of solving the ODE, but I need a little help regarding the first t. From what I understand from lectures, all of the 't' terms need to be in...

I am trying to see if I understand the convolution process correctly. This is from the solved example of my prof's notes: x[n] = u[n] and h[n] = a-nu[-n] for 0<a<1 As expected the first step was y[n] = x[n]* h[n] = Ʃ h[k]x[n-k] -∞<k<∞ = Ʃ a-ku[-k]u[n-k] -∞<k<∞ From my...

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...

I'm trying to get my head around the step function and the energy states of the quantum well. What I've got so far is this: The density of states for an electron confined in one direction by the potential barriers of the well, but free to move in the other two directions in the place of the...

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 Consider the following initial value problem: y''+4y = 9t, 0<=t<2 ...0, t>=2 Find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) Homework Equations The Attempt at a Solution I am just having trouble with the step...

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)?

Homework Statement Find the Laplace transform of f(t) where f(t)={ 3 if 0<=t<2 2t^2+2 if 2<=t<3 -4 if t>=3 Homework Equations The Attempt at a Solution We where taught to approach this from a "turn-off, turn-on" strategy where...

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)