plucked string Fourier | Desmos

Expression 4: StartFraction, 4 Over pi , EndFraction Start sum from "k" equals 0 to "k" Subscript, "m" "a" "x" , Baseline , end sum, StartFraction, left parenthesis, negative 1 , right parenthesis Superscript, "k" , Baseline Over left parenthesis, 2 "k" plus 1 , right parenthesis squared , EndFraction sine left parenthesis, left parenthesis, 2 "k" plus 1 , right parenthesis "x" , right parenthesis cosine left parenthesis, left parenthesis, 2 "k" plus 1 , right parenthesis "t" , right parenthesis

4

Expression 5: "u" equals StartFraction, 4 Over pi , EndFraction sine left parenthesis, "x" , right parenthesis cosine left parenthesis, "t" , right parenthesis

5

Expression 6: "u" equals StartFraction, negative 4 Over 9 pi , EndFraction sine left parenthesis, 3 "x" , right parenthesis cosine left parenthesis, 3 "t" , right parenthesis

6

Expression 7:

7

8

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