Hi, I'm working with series solutions of differential equations and I have come across something that has troubled me other courses as well. given that
\begin{equation}
\sum_{n=0}^{\infty} c_{n+2}x^n+e^{-x} \sum_{n=0}^{\infty}c_{n}x^n \\
\text{where}\\...
Homework Statement
An em wave in free space has an electric field vector E = f(t-z/c0)x where x is a unit vector in the x direction and f(t)= exp(-t2/τ2)exp(j2πv0t). Describe the physical nature of this wave and determine an expression of the magnetic field vector.
Homework Equations...
Z [x (n − n0)] = z-n0X(z);
y[n]+1/2y[n-1]=x[n]
→y[n+1]0+1/2y[n]=x[n+1]
Z-transform and get
→ z1Y(z) + 1/2z0Y(z)=z1X(z)
→ (z+1/2])Y(z)=zX(z)
given that H(z) = X(z)/Y(z)
z/(z+1/2)=X(z)/Y(z)=H(z)
I hope this is correct now?
though I'm still not getting the initial point part.
well in the textbook I'm using it's written
Z [x (n − n0)] = z-n0X(z);
and if Z(Y[n])= Y(z) then Z(Y[n+1])= z1Y(z)
that's gives me y[n]+1/2y[n-1] = z0Y(z) + 1/2z-1Y(z)
that's where I go Y(z) = 1+1/2z-1. I don't understand where I am going wrong
I'm not so sure about the time shifting theorem, but I used the Transfer function H(z)=Y(z)/X(z). my X(z) is z/(z-a) and I tried Y(z) to be z+1/2 but I'm unsure. after that I supposed to sketch it's Zeros and poles. Am I on the right track?
Homework Statement
x[n] = anu[n]
A discrete system
y[n] = −1/2y[n − 1] + x[n];
where x[n] and y[n] in- and output of the system, respectively.
Find the system transfer function H(z), and sketch its zeros and poles
in the z-plane
Homework Equations
u[n] is the unit step function...
thanx I solved it doing it your by changing to spherical and got 0 on both sides, but the question still remains, is there a theory that says something about if you have an odd function and a symetric surface then the integral is automatically 0. Like no matter what function as long as it's...
I've used sperical coordinates on the right side and I get 0 unless I did something wrong,
but I'm more concerned about the left side
I've changed it a bit but the question still remains, can I just say its = 0 becoz the surface is symmetrical and odd functions have double integral =...
Homework Statement
verify Stokes theorem for the given Surface and VECTOR FIELD
x2 + y2+z2=4, z≤0 oriented by a downward normal.
F=(2y-z)i+(x+y2-z)j+(4y-3x)k
Homework Equations
∫∫S Δ χ F dS=∫ ∂SF.ds
the triangle is supposed to be upside down.
The Attempt at a Solution
myΔχF =...
thanx I solved it! I expressed my v as √g r sinθ and my height as r(1+sin(θ) and then put it in the consevation of energy equation!
,but there was a part b) in the question. if you assume the object goes out off the loop at any given P and lands on the loop again at E which is the same height...
v = sqrt(g r sin (theta))
0.5mv*v = mg h
h= r sin (theta) /2
then i use my equation
1/2* kx^2 = 1/2m g sin (theta) + 1/2mg sin (theta). but i get my 1/2 kx^2 > mgr. should that be possible?
if I add theta then I will have two unknowns, h and theta, and since now i can find the speed of v at horizontal diameter. mgsin 45=mvv/r but how will it help?
mg sin(theta) = ma
the forces that act are mg downwards and centripetal in the radial direction. then our mg sin must be our normal force which also points in the radial direction,am I going in the right direction?
that's all that is the question, but I tried using Forces. the conditions to stay in the loop on top is mg + n = mv2/r where n=0 because it doesn't touch the loop. then v= √gr but that's just on the top, I don't know how to do it in another random area . the point it let's go it becomes free...