I still cant find the equation using laplace transform
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I think I would agree with both of you. It seems most people would consider the single sided Laplace transform (integral from zero to infinity, not negative infinity to infinity). This is equivalent to the full Laplace transform when multiplying by the Heaviside function which zeros out the other half of the full integral. Also, most would assume initial condition of zero on the state variable, unless otherwise specified.Perhaps steveb might help us out.
I would agree with this statement. The main problem I have is that most engineers don't realize they are assuming a convention in a large fraction of situations. Either they never learned it in anything resembling a rigorous way or they have long since forgotten it. I suspect it is a mixture of both. I think teachers at all levels make an unconsious mistake that if you teach something with rigor when it is first presented that the student will forever be aware of the assumptions and limitations. I know, in my case as a student, this was a really bad assumption. Like most students, I had a hard time caring about regions of convergence and whatnot in part because it seemed like extraneous stuff that was only of theoretical significance. But also because few courses do more than just brush over the stuff in passing. I think it would be much better if courses routinely ensured that problems in which such details are important constitute a noticeable portion of the assignments and exam problems. In addition, on the handful of occasions in which a follow-on course spent the first class doing a quick but thorough review of the entire preceding course to be extremely useful because I could then see how some of the subtle points of the foundational work from the beginning of the course tied in with other parts of the course in behind-the-scenes ways.I think from a mathematician's point of view, engineers are always sloppy when describing these situations, but I think a better way to say it is that there is an assumed convention in place when engineers are talking about these problems.
Yeah, we did kinda get off on a tangent. But we're expecting to see something from you showing what you've done so far and where you are having problems. It's hard to give good help without knowing where the problem lies.Thanks for the help guys. But i still dont get how to arrive at the equation with cos, sin and exp in there!
Read the question again, carefully, and ask yourself why you think Vout is the voltage across the resistor. Remember, "voltage across" means the voltage on one side relative to the voltage on the other. The output voltage is the voltage on the top right node compared to the voltage on the ground node. Which component can be described as having that same voltage across it?okay! last question, what do you mean by "Is the output voltage the voltage across the resistor?" Is'nt that what the question stated? Is it the voltage across the capacitor instead?
Okay, I went back and read the question again, carefully, and I see where the confusion is coming from. The statement in the hint (which I overlooked) does state that the output voltage is the voltage across the resistor. But the diagram clearly shows it being the voltage across the capacitor and this is the voltage that the given answer represents.Read the question again, carefully, and ask yourself why you think Vout is the voltage across the resistor. Remember, "voltage across" means the voltage on one side relative to the voltage on the other. The output voltage is the voltage on the top right node compared to the voltage on the ground node. Which component can be described as having that same voltage across it?