Recent content by Jonas E

I have now tried that for both (f * g) and (g * f), but in both cases I get the correct answer for case 3 (t > 2), when I'm trying to solve for case 2: (f * g) = ∫[ e^(-τ) - e^(-2τ) ] * [ u(t - τ - 1) - u(t - τ - 2)]dτ I find that for case 2: t - τ - 1 > 0 Λ t - τ - 2 < 0 which gives me: t...

I don't think I understand. I get the right answer for (g * f) if I integrate from 0 to (t - 1) instead, but I don't understand why. Could you please explain?

Homework Statement y'' + 3y' + 2y = r(t), r(t) = u(t - 1) - u(t - 2), y(0) = y'(0) = 0. I need to solve this by convolution, which I know is commutative. The problem is that my calculation gives (f * g) =/= (g * f). Could someone please tell me where my mistake is? Homework Equations...

Ah, thanks a lot for the help. So, the mistake was that s(s + 4)Ỹ should have been (s^2 + 4)Ỹ instead? It seems I accidentally calculated 4ℒ(ỹ) to be 4sỸ

Sorry, @Mark44 , I meant T by t - 1, not r - 1. Here are the steps I did: y'' + 4y = 8t^2 * [1 - u(t-5)] = 8t^2 - 8t^2 * u(t-5) ỹ'' + 4ỹ = 8(T + 1)^2 - 8(T + 1)^2 * u(T - 4) ỹ'' + 4ỹ = 8(T^2 + 2T + 1) - 8(T^2 + 2T + 1) * u(t - 4) I use Laplace on both sides and get: s(s + 4)Ỹ - s - scos(2)...

Homework Statement y'' + 4y = 8t^2 if 0 < t < 5, and 0 if t > 5; y(1) = 1 + cos(2), y'(1) = 4 - 2sin(2). Use the Laplace transform to find y. Homework Equations t-shift, s-shift, unit step function. The Attempt at a Solution I have been trying to solve it for hours, but keep getting the wrong...

EDIT: Ok, sorry again, but I just found out what I did wrong: When taking the square root, I forgot that there would be two answers. The negative one turned out to be the correct one. Thanks for helping me out figure out my original problem! Sorry, the original post was just part of the...

Sorry, I forgot to square the voltage. But is this correct then: w(t) = 1/2 * C * [v(t)] ^2 ? I couldn't understand the wikipedia article. You see, I used this formula, but it doesn't give me the right answer

Thanks for the reply. Could you also tell if the energy in a capacitor at time t equals half of its capacitance times its voltage at time t? So w(t) = 1/2 * C * v(t) ?

Homework Statement I have the circuit in the picture below, and using KCL and KVL I found that the voltage over the 80k resistor is 0. However, I don't understand why this is correct. Can someone explain why there is no current through it? Homework Equations None The Attempt at a Solution I...

I understand now, thanks a lot for clearing it up!

Don't know how to edit the original post, so I'll post the edit here: I set p(t) = V(t)^2 / R and integrate from 0 to t. This gives me the following expression: w(t) = -1/125 * (e^(-100t) - 1), which I set equal to 0.25 * 8 * 10^-3 in order to find the time. (0.25 because I need to find how...

Sorry, it should say v^2 in the energy formula, but that doesn't change anything since I used the other formula anyway. My problem is that the 1st formula (which I mistyped) gives a different answer than the second one (which is the one I used).

Homework Statement I have an RC circuit where C = 0.4 * 10^-6, R = 50k Ohms. The problem says: "Find the length of time required to dissipate 75% of the initially stored energy." Homework Equationsenergy 1: 1/2 * C * v(t) energy 2) w = ∫p(t)dx, from 0 to t The Attempt at a Solution This is...

Here is my problem: when trying to find Rth for a circuit with dependent sources, I excite the circuit a voltage Vo, and then proceed to find the resulting current Io. Finally, I use the equation Rth = Vo / Io, with a plus (+) sign. The way I see it, Io enters the positive side of Vo, so the...