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Equations f(x 1 )= 2*sin(1*x)

Equations f(x 1 )= 2*sin(1*x). Parameters: Amp freq 2 1. Equations f(x 1 )= 2*sin(1*x) f(x 2 )= -1*sin(2*x). Parameters: Amp freq 2 1 -1 2. Equations f(x 1 )= 2*sin(1*x) f(x 2 )= -1*sin(2*x) f(x 3 )= .67*sin(3*x). Parameters: Amp freq 2 1 -1 2 0.67 3. Equations

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Equations f(x 1 )= 2*sin(1*x)

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  1. Equations f(x1)= 2*sin(1*x) Parameters: Amp freq 2 1

  2. Equations f(x1)= 2*sin(1*x) f(x2)= -1*sin(2*x) Parameters: Amp freq 2 1-1 2

  3. Equations f(x1)= 2*sin(1*x) f(x2)= -1*sin(2*x) f(x3)= .67*sin(3*x) Parameters: Amp freq 2 1-1 2 0.67 3

  4. Equations f(x1)= 2*sin(1*x) f(x2)= -1*sin(2*x) f(x3)= .67*sin(3*x) f(x4)= -.5*sin(4*x) Parameters: Amp freq 2 1-1 2 0.67 3-0.5 4

  5. Equations f(x1)= 2*sin(1*x) f(x2)= -1*sin(2*x) f(x3)= .67*sin(3*x) f(x4)= -.5*sin(4*x) f(x5)= .4*sin(5*x) Parameters: Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5

  6. Sum the first five terms Equations f(x1)= 2*sin(1*x) f(x2)= -1*sin(2*x) f(x3)= .67*sin(3*x) f(x4)= -.5*sin(4*x) f(x5)= .4*sin(5*x) Parameters: Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5 watch the magenta line as we sum the first ten terms

  7. Sum the first ten termsGiven f(xi) = Amp * sin (freq * x)The List of parameters contains the same information as the magenta line Equations f(x1)= 2*sin(1*x) f(x2)= -1*sin(2*x) f(x3)= .67*sin(3*x) f(x4)= -.5*sin(4*x) f(x5)= .4*sin(5*x) f(x6)= -.33*sin(6*x) f(x7)= .29*sin(7*x) f(x8)= -.25*sin(8*x) f(x9)= .22*sin(9*x) f(x10)= -.2*sin(10*x) … Parameters: Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5-0.33 6 0.29 7-0.25 8 0.22 9 -0.2 10 It is much easier to list the parameters then graph the sum of the functions

  8. Sum the first ten termsGiven f(xi) = A*sin(f*x)The list of parameters contains the same information as the magenta line Parameters: Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5-0.33 6 0.29 7-0.25 8 0.22 9 -0.2 10 = It is much easier to list the parameters then graph the sum of the functions

  9. The first ten terms of f(xi) = A*sin(f *x) in Parameter Space Parameters: Amp freq 2 1-1 2 0.67 3-0.5 4 0.4 5-0.33 6 0.29 7-0.25 8 0.22 9 -0.2 10

  10. Amplitude versus Frequency(aka amplitude spectrum) Amplitude versus Distance = Space Domain Frequency Domain (1/distance )

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