Homework 6 collaboration area
From Mnestero:
On 6.4 prob 10 I am getting a pretty intense solution that is difficult to graph. Am I on the right track? How in depth are we supposed to graph the solution?
Response from Mickey Rhoades Mrhoade
I thought the same thing. My solution is pretty intense as well. It seems like there is the portion from the initial conditions which is e-2t - e-3t and then there is the portion from the impulse function which is added beginning at pi/2, epie-2t - e3pi/2e-3t and then there is the portion of the output due to the cosine input beginning at pi. This section looks like a sin/cos wave inside an exponential envelope. Did anyone else come up with something different? -Mick
Remark from Steve Bell:
That's life for engineers. The solution corresponds to a hammer hit on a spring-mass system (with damping) at time pi/2 followed by turning on a vibration force at time pi. You will note that the solution you get, although piecewise defined, is continuous. The velocity jumps at the hammer hit. After you experience trying to graph it with your bare hands, I will show you how to use maple to graph these things.
Remark from Steve Bell:
I got a question about p. 231: 14a in class today. Split the integral up like the book suggests. For the integral
$ \int_{np}^{(n+1)p} e^{-st}f(t)\ dt, $
make the change of variables
τ = t + n'p
and take it from there. In part b, you just need to apply the formula derived in part (a) to the function they give you.
Question from Luo Shibo;
On 6.4 problem 14(b): half wave rectifier
I can get the f=sin(wt) for 2n*pi<t<(2n+1)*pi ,and f=0 for (2n+1)*pi<t<(2n+2)*pi. But I have no idea about how to combine them together, I mean combine them into one equation: f=sin(wt-xx)*u(t-xx) such kind of form. Could someone give me a hint?
