Recent content by GuiltySparks

Hi all, I had a thought earlier about magnetic forces. If there's a magnet attached (at rest) to my fridge, then there is a magnetic force on the magnet towards the fridge and vice-versa. This force stops the magnet from falling because of the frictional force between the magnet and the...

Homework Statement Find the convolution of g(x) = e^{-πx^{2}} with itself from -∞ to ∞ using the definition of convolution, not the Fourier Transform. The Attempt at a Solution See my attachment. My professor said that you have to use integration by parts, but I keep getting stuck...

I've attached a copy of the problem and my attempt at a solution. This seems like a relatively straightforward question to me, but my answer seems to be the exact opposite of what the answer key says. I reach the conclusion that the answer is C, but the answer is apparently D. I'm...

To clarify, both DC sources in the circuit are step inputs? If so, you need to represent them as a heaviside function in the s-domain (or u_0(t)), like I did in the previous derivation. Though, I do have the sneaking suspicion that you are incorporating these into the circuit to account for the...

Yes, we can use the definition of sinh and cosh. Hyperbolic sine: (e^2x - 1)/(2e^x) Hyperbolic cosine: (e^2x + 1)/(2e^x) 3(e^-t)[(e^2rad3(t) + 1)/(2e^rad3(t))] + (4/rad3)(e^-t)[(e^2rad3(t) - 1)/(2e^rad3(t))] =3(e^2rad3(t) + 1)/(2e^(rad3(t)+1)) + (4/rad3)(e^2rad3(t) - 1)/(2e^(rad3(t)+1))...

Paul's Calculus Notes is a great resource. Use it myself.

Remember your unit circle. Taking the inverse cosine of (1/pi) points to one of two possible triangles that lie on this circle. From the argument, we know that the x-component of this circle will be 1; the hypotenuse will be pi. Remember that the hypotenuse will always be positive but the x- or...

Let's complete the square of the polynomial equation to get it into a form that we can use. s^2 + 2s -2 = (s+1)^2 -3 Now, we have 3s/[(s+1)^2 -3] + 7/[(s+1)^2 -3] = 3(s+1)/[(s+1)^2 -3] + 4/[(s+1)^2 -3] invLaplace => 3(e^-t)hcos(rad3*t) + (4/rad3)(e^-t)hsin(rad3*t)

Doing it was actually pretty informative for me, also. I realized that if you take your source to be Vin/s, then that assumes the voltage on the circuit is always Vin for all time t. You would then need to account for initial conditions when doing the Laplace Transform; incorporating a heaviside...

I worked out the solution and attached it. Notice that I assume at time t = 0 a DC step function is applied. You will have to minimize the amplitude of the trigonometric function. To do this, compute the partial derivatives of the amplitude A with respect to L, R, and C and set them equal to...

First of all, let's use some of our intuition regarding circuits - intuition that every electrical engineer should have, that is - and predict the activity of this circuit. Notice that the input voltage is Vi/s; this corresponds to a DC signal of magnitude Vi that is applied to the circuit for...