Recent content by j3dwards

I'm confused - how is there a current flowing through the inductors at the moment that the switch opens if you just said no current can flow? Is this because, like you said, the coils have stored energy and this energy is producing in emf which in turn creates a current? Also, I'm guessing...

Yes, I have attached the diagram drawing

Homework Statement The circuit consists of three identical light bulbs and two identical coils, connected to a DC current source. The ohmic resistance of the coils is negligible. The system is left to settle into a steady state and then the switch S is opened. Describe and explain in as much...

You get the eigenvalues in the diagonal elements in the diagonalised matrix. Please explain, I really don't understand and my exam is soon!

Homework Statement Explain in your own words why the product of eigenvalues of any diagonalisable N × N matrix A must equal the determinant of A. Homework Equations MT=M-1 The Attempt at a Solution So what I do know: the determinant measures the change in area of the unit square under the...

Homework Statement Solve the following initial value problem using Laplace transforms: y' + 4y = 3t3 e−4t ; y(0) = 0 . Useful information: Recall that the Laplace transform of y 0 is pY − y(0), where Y is the Laplace Transform of y. The Laplace transform of tk e−at is k!/(p + a)k+1 . Confirm...

Okay perfect, thank you so much.

I'm not really sure how to use a(-x) = a(x) or -a(x) to check. Do I literally just make the rhs of the equation equal to negative of what it is a see if it comes out with the same answer?

I did check originally, but I'm just quite unsure about odd and even functions so I was just asking to make sure so that for that exam, I knew the correct method.

Yes it does add up. So I am correct?

From my workings, I believe I am correct? I can't see any errors myself, so was wondering if you could help me.

Homework Statement Split the function f(x) = ex + πe−x into odd and even parts, and express your result in terms of cosh x and sinh x. Homework Equations f(x) = 0.5[f(x) + f(-x)] +0.5[f(x) - f(-x)] The Attempt at a Solution So i know that: ex = 0.5[ex - e-x] + 0.5[ex + e-x] = sinh(x) +...

Homework Statement Compute the average value of the function: f(x) = δ(x-1)*16x2sin(πx/2)*eiπx/(1+x)(2-x) over the interval x ∈ [0, 8]. Note that δ(x) is the Dirac δ-function, and exp(iπ) = −1. Homework Equations ∫ dx δ(x-y) f(x) = f(y) The Attempt at a Solution Average of f(x) = 1/8 ∫from...

Oh I forgot to add in the fP = -3π. So why are there 2 free parameters, do you know? Is it because the equation is twice differentiated leaving two constants? Thank you

Homework Statement Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why? Homework Equations f = fH + fP where fH is the homogeneous solution and fP is the particular solution. The Attempt at a...