symsum wave harmonics along a string

PLEASE CLOSE THIS

[JDilla]

Not too sure why my post has been formatted like that?

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

Answer 1

[Walter Roberson]

In order to use symsum() you would need to be using a symbolic formula with at least one symbolic variable in it. There is nothing in your definition of u that is obviously a free variable. Is w_n your free free variable? Perhaps, but you have written your Fw_n in terms of w_n and tau with tau not defined.

[JDilla]

yeah w_n is available to be anything (for the moment).

Still not working!

[JDilla]

would cumsum work?

[JDilla]

Nope! cumsum does not work haha

[Walter Roberson]

What precisely is it that you would like to total? You show a double-nested loop and you show a plot inside one of the loops. You have k=5: is k the harmonic number, and for "first 5 harmonics" you would like to add another level of nested loop over k ? Or is w_n your harmonic number?

"My desired output would be a symbolic function P in the parameters R, and S. It would be the sum of a symbolic function Q over R, S, and H over H from 1 to 5 where H is the harmonic number. Q(R,S,H) is defined as ...." ???

[JDilla]

Right, I've attached the expression for the net displacement of the string I am modelling. The net displacement is the sum of the standing waves

The source, which is applied at distance X_s (denoted as Xs in the expression) is given by F(w_n) which I included earlier. W_n is the frequency of the standing waves. I do not pick the frequency, I pick the tuning parameter, which determines the angular frequency and thus the overall form of the wave. Tuning paramter = tau. I can pick this to be whatever.

I need to end up with seperate harmonics (different because of different tuning parameters) and plot them, and then sum them using the expression provided

n denotes the harmonic number. Something like n=1:4 somewhere in the loop for the first 4 harmonics for example. (I want to explore particular harmonics).

I hope this makes sense. The last term is cos(w_n*t), not w*n*t.

[Walter Roberson]

Your first sin() appears to have x subscript s. What is that? Your second sin() has x without the subscript, and I cannot assume that x(s) and x are the same because if that were the case then your two sin() terms would be the same and you would have written the expression as sin^2() rather than as two terms.

[JDilla]

"The source, which is applied at distance X_s (denoted as Xs in the expression"

There is a source applied to the string, eg, plucking a guitar string at a distance of X_s. It can be any number.

Answer 2

[JDilla]

To word this differently, I have code that describes ONE standing wave. I want 5 standing waves, of different angular frequencies (w_n) as subplots. Whilst I cannot pick the angular frequency, I can change tau. The expression of the source which determines tau is Fw_n = exp[-(w_n*tau)^2/4]. Fw_n is the expression of the source, ie, plucking or strumming the string, that is applied at a distance X_s

Then, using the expression in the picture, calculate the sum of the standing waves, and then plot this as well. The sum of the standing waves should generate a different shaped wave.