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?