# fcn

1. ### Finding Marrginal Density Fcn From Join Density Fcn

We have two random variables X,Y with continuous dist. Its join density function is f(x,y) and marginals fX(x) and fY(y). I need to show that the integral from -infinity to infinity with respect to y of the joint density function is the marginal fX(x), and the same with respect to x is the...
2. ### Spring-Mass system (with damping force AND impressed force). Find Position fcn.

Here is the problem: A spring is such that a 2 pound weight stretches it 6 inches. There is a damping force present with magnitude the same as the magnitude of the instantaneous velocity. An impressed force f(t) = 2 sin 8t, acts on the spring. At t= 0, the weight is released...
3. ### Shifted fcn...

Given: x(t) = u(t) - u(t-10) calculate: Int(x^2)tdt Am I thinking about this correctly... u(t) is 0 from neg. infinity to 0, and 1 after. u(t-10) is the same thing just shifted to the right to "turn on" at 10. So in effect we have a rectangle of amplitude 1 with bounds from 0 to...
4. ### Graph of a fcn...

Hey guys, This is more of a generalized question than one from the textbook etc.. Can someone explain to me how you could take a graph of the derivate or f'(x) for example and from that, graph the original function? Im having trouble going in the opposite direction... Thanks in advance! Chris