In article: <email@example.com> firstname.lastname@example.org (Brian P. Davis) writes: > > I've been given a problem, and I'm stumped. My professor has assigned us > the problem of determing the y value of the following equation when the > time, t, is not equal to 0. > > y = (A cos(wt) + B sin(wt)) sin (wx/c) > > I purposely left off the subscripts for readability. A should be A sub n > B should be B sub n, and the same for y and w. > > We know the following information: > frequency = 100Hz > length of string = 50cm > string struck by mallet at 12.5 cm (or length / 4) > time increment is 0.0001s > > I've already done the integration and have equations for A sub n > and B sub n. > > My biggest problem right now is what to do with x. Is it a constant > value (i.e. length / 4) or do you have to calculate for every possible > value of x? If the latter is the case, how do you come upon a final > answer for y? Or am I just way off base? > > Thanks for any help, > Brian >
I assume that (x,y) are coordinates of points on the vibrating string. In that case you find the displacement y for any given x. Clearly y will vary for any value you assign to x, but you find what a particular point on the string is doing, by entering its x-value in the equation and keeping it constant while you see what happens to y as t changes. I should have thought that the x=12.5 point will be used in finding the constant of integration - but I am not sure how the original equation was derived.