Step function Definition and 136 Threads

Homework Statement Express f(t) = e^t, 0<t<2, using the unit step function 2. The attempt at a solution e^t*u(t-2) is an expression for a graph of the function that is zero until t=2. My guess is e^t*u(t+2)

I'm not sure how to solve a differential equation with unit step function, for example: x'' + 2x' + x = 10t*u(t), where x(0)=1 and x'(0)=0 Do I just ignore the u(t) and solve it regularly by normal integration?

Homework Statement The function f(t) is defined for t>=0 by f(t) = 1 for 0<= t <= 1 , t-2 for 1 <=t <= 2 and 0 for t >2 Express f(t) in terms of the Heaviside function and hence or otherwise find L(f(t)), the Laplace transform of f(t) Homework Equations The Attempt at a...

[SOLVED] Dirac delta function and Heaviside step function In Levine's Quantum Chemistry textbook the Heaviside step function is defined as: H(x-a)=1,x>a H(x-a)=0,x<a H(x-a)=\frac{1}{2},x=a Dirac delta function is: \delta (x-a)=dH(x-a) / dx Now, the integral: \int...

Homework Statement I'm having a bit of difficulty understanding the unit step function For example f(t) = 6u(-t) + 6u(t+1) - 3u(t+2) t = -1 Homework Equations The Attempt at a Solution If t = -1 then the way I would do the problem is say that if u(t) returns a negative number...

The question says to sketch the signal (t-4)[u(t-2)-u(t-4)]. I know that the inner part is a delay of two and a delay of four, but I don't know what to do with the (t-4)...does it have anything to do with the slope?

Given... (2s^{2}+1)e^{-s} ------------------ (s - 1)(s^{2} + 4s + 5) Find the inverse Laplace Transform. I am unsure where to start and am just looking for a little direction, not an answer. From past experience, I am assuming I will have to rewrite this in another form...perhaps by...

Homework Statement Compute the Z-transform of x[n] = (0.5)^{-n} * u[n-1] And find the ROC (Region of Convergence) Homework Equations Z-Transform for discrete time x(z) = \sum_{n=0}^\infty x[n] * z^{-n} The Attempt at a Solution To solve this, I used the definition of...

Homework Statement Let f be a function that is integrable on [a,b] and bounded by 0 \leq f(x)\leq M for some M. Prove that f^{2} is also integrable on this interval. Homework Equations We've done many problems with step functions s(x)\leq f(x) \leq t(x), where s(x) and t(x) are...

How do you represent a unit step in MATLAB as ONE function, y , for example. I know only how to graph multiple vectors on top of the same graph (using hold on/off) and getting the graph output, but i can't represent it as a function itself. Any ideas?

Integration with a step function?? Homework Statement How do you go about integrating a function that has parameters "x" and "delta" where "delta" is a step function of "x" (delta is 1 for x>0, 0.5 for x=0, and 0 for x<0)?? I don't remember doing anything like this in any of my math...

Homework Statement Find the laplace transform of u(-t) Homework Equations The Attempt at a Solution For u(t), the laplace transform of it is 1/s, basically taking the integral of e^-st from 0 to infinity. In this case, since the unit step function approaches from the negative...

Homework Statement What is the Laplace transform of f(t) = t^2 - 18 for 0 < t < 3 and f(t) = (t-3)^2 for t>3?Homework Equations Laplace Transforms 3. Work Using Heaviside/step function, made equation into: f(t) = t^2 - 18 + u(t-3)( (t-3)^2 - (t^2-18) ) Then, using Laplace transforms...

Homework Statement I have an equation that has the following values at different intervals: It is: r when 0<x<2Pi r - (1)d when 2Pi<x<4Pi r - (2)d when 4Pi<x<6Pi And so on. I want to find a function that encompasses this whole function. Unit functions / discontinuity functions are fine; as...

could you give me the method of sketching the graph of a step function here is an example: N(t)=25(2||t+2/2||-t) thanks a lot for your help

Hi there, I'm stuck on getting my step function set up. the function is: f(t)= 0, t<0 (a/b)*t, 0<t<b a, t>b where a and b are just constants. Here's my step function of the first two intervals...the first one I didn't do anything to it since it's zero, so I got...

Suppose U(x) is the step function and \delta(x) is its derivative. Find \int^{6}_{-2}(x^{2}-8)\delta(x)\dx . I know \delta(x) = 0 for all x except x = 0 . So at x = 0 v(x) = - 8 . After this step, how do we get \int_{-2}^{2}(x^{2}-8)\delta(x)\dx +\int^{6}_{2}(x^{2}-8)\delta(x)\dx =...

Dear All, I have a moderate knowledge of mathematics and need help on an integration question. How would I go about integrating a step function: H(K - Z), when the integral is from K=Z to infinity. Please advise, your help would be much appreciated. Suz

f(x) = <x-a>^1 - <x-2a>^1 - a<x-3a>^0 this is a diagram of heaviside step function.does anybody has any website regarding this materials so that i can get to learn such as why is it power of one and power of zero plssss thanx very much

Is this the proper way to write the Heavenside function for the following conditions: g(t) = t if t <= 8pi 8pi if t > 8pi Heavenside: g(t) = t + (8pi - t)*U(t-8pi)

How do you go about convolving when x(t) = u(t-1)? Can you just make the limits of integration 1 to t instead of 0 to t?

how can I calculate the Fourier transform for unit step function: v(t)=1 where 0=<t<+infinity v(t)=0 otherwise I applied the general definition relation for FT: v(w)=integral(v(t)*e^-jwt) ; - infinity<t<+infinity but i had v(w)=infinity due to the term infinity-displaced e^(+jwt)...

Cable System - Step Function Hi, I want to do an experiment using two dissimilar ropes in my basement and see if I can produce some results using a rope analysis. Here’s the set up. I want to tie a light rope to a heavy rope, and be able to characterize the curvature the system takes on. I...

Find the FOurier Series in terms of \phi_{n} = \sin(nx) of the step function f(x) = 0 for 0 \leq x \leq \frac{1}{2} \pi [/tex] f(x) =1 for [itex] \frac{1}{2} \pi < x \leq \pi now i have no problem finding the series for each branch. But how would i combine them? for the 0 to 1/2 pi...

Find the Fourier Series in terms of \phi_{n} = \sin{nx} of the step function f(x) = 0 for 0 \leq x \leq \frac{1}{2} \pi = 1 for \frac{1}{2} \pi < x \leq \pi Solution Fourier Series is \Sigma c_{n} \phi_{n} and for hte interval for x between 0 and 1/2 pi c_{n} =...

hello maths experts is the following true? http://img9.imageshack.us/img9/4596/int15oe.jpg graphically, this is how i view it http://img9.imageshack.us/img9/179/int28ut.jpg

heaviside or step function I don't quite understand how to add step functions and would like to get that down before this one class begins. Does anyone know a good tutorial or a helpful site or a book with answers? Thank you.

I have some trouble wrapping my head around singularity One of assignment question is to show that the unit function is not defined at 0. To do that, I need to show \lim_{\Delta\to0}[u_{\Delta}(t)\delta(t)]=0 \lim_{\Delta\to0}[u_{\Delta}(t)\delta_{\Delta}(t)]=\frac{1}{2}\delta(t)...

I would like to invite comment to the near step function below. \Mvariable{step(x)}=\frac{{e^{-\frac{\gamma }{{x^2}}}}}{{\sqrt{1-\frac{{e^{-\frac{\gamma }{{x^2}}}}}{{x^2}}}}} the above function evaluates to nearly 1 for |x|>1 and nearly zero for |x|<0.3 for gamma =...

I am given an ideal OP-AMP like this (R-resistor, Cap-capacitor): ____+Cap-_ | | ___R____|__|\______|_____ + | -|/ + | V in | V out - | | | |_________|______________ - and V in is...

Hey I was wondering if someone would check my work on this problem: Note: {\cal L} = Laplace {\cal U} = Unit Step Function {\cal L} \{ \cos(2t) \,\,\, {\cal U} (t - \pi)\} =e^{-\pi s} {\cal L} \{ \cos(2(t + \pi)) \} =e^{-\pi s} {\cal L} \{ \cos(2t + 2\pi) \} =e^{-\pi s}...

I just want to check if I got this right. Given this graph, I need to define a step function: | ---------| C | _________|_______________ | -C |_________ | So, my definition is: C[-u(t) + u(-t)]. Thanks for checking this.

Heaviside? HELP hey there peeps, could u guys help me out with heaviside step function..cu zi don't understand anything bout how it works and how to apply to a particular problem... could u guys explain in detail how to solve the next equations using heaviside: exp[-2s] F(s)=...

Let f (x) = 1 if 2<=x<4 2 if x =4 -3, if 4<x<=7 Prove that this function is integrable on [2,7], state its value and prove that it is what you say it is. Obviously integral of f from [2,7] is -7. but its proof and the integrability have me and my friends snagged. Suggestions anyone? SO...

My second course in analysis and i have a problem which i can't understand Let f (x) = 1 if 2<=x<4 2 if x =4 -3, if 4<x<=7 Prove that this function is integrable on [2,7], state its value and prove that it is what you say it is. Obviously integral of f from [2,7]...

[SOLVED] Derivative of unit step function How does one do this, for example x= e^(-3t)u(t-4); how do you get x' ??