REM nm3bbc.bas - jackord@kw.igs.net - 28 Mar 07 - BBC Basic v5.50b
      REM string of length 8d, clamped at both ends
      REM equal point masses at intervals of d
      REM finite and infinite Fourier Sine Series representations of
      REM   "Pluck" and "Pulse" initial displacements
      
      *FLOAT64
      INSTALL @lib$+"WINLIB5"
      
      REM Initialize Window
      b1% = FN_button("Pluck FFSS", 10, 5, 90, 20, FN_setproc(PROCp1), 0)
      b2% = FN_button("Pulse FFSS", 105, 5, 90, 20, FN_setproc(PROCp2), 0)
      b3% = FN_button("Pluck FSS", 200, 5, 90, 20, FN_setproc(PROCp3), 0)
      b4% = FN_button("Pulse FSS", 295, 5, 90, 20, FN_setproc(PROCp4), 0)
      WindowWidth=396
      WindowHeight=240
      VDU 23,22,WindowWidth;WindowHeight;8,15,16,128
      n=8: DIM y(8): DIM b(8)
      OFF: VDU 5
      
      REPEAT
        WAIT 1
      UNTIL FALSE
      QUIT
      
      DEF PROCp1: kk=1: ff=1                         : REM Pluck FFSS
      
      DEF PROCp2: kk=2: ff=1                         : REM Pulse FFSS
      
      DEF PROCp3: kk=1: ff=2                         : REM Pluck FSS
      
      DEF PROCp4: kk=2: ff=2                         : REM Pulse FSS
      
      IF kk=1 THEN
        FOR i=0 TO n/2
          y(i)=80*i: y(n-i)=y(i)
        NEXT i
      ELSE
        FOR i=0 TO n: y(i)=0: NEXT i: y(n/2)=320
      ENDIF
      FOR i=1 TO n-1 STEP 2
        IF ff=1 THEN
          b(i)=0
          FOR j=1 TO n-1
            b(i)=b(i)+2*y(j)/n*SIN(PI*i*j/n)
          NEXT j
        ELSE
          IF kk=1 THEN
            b(i)=160*(4/PI/i)^2*SIN(i*PI/2)
          ELSE
            b(i)=160*(8/PI/i)^2*(SIN(PI*i/2)-SIN(PI*i*3/8))
          ENDIF
        ENDIF
      NEXT i
      CLS:GCOL 12: MOVE 8, 90                        : REM Displacement
      FOR i=1 TO n
        DRAW 12+96*i, 90+y(i)
      NEXT i
      FOR i=0 TO n
        CIRCLE FILL 12+96*i+2, 90+y(i)-2, 12
      NEXT i
      GCOL 10                                        : REM Components
      FOR i=1 TO n-1 STEP 2
        MOVE 12, 90
        FOR j=1 TO 48*n
          DRAW 12+2*j, 90+INT(b(i)*SIN(PI*i*j/n/48)+1)
        NEXT j
      NEXT i
      GCOL 9: MOVE 12,90                             : REM Superposition
      FOR j=1 TO 48*n
        z=0
        FOR i=1 TO n STEP 2
          z=z+b(i)*SIN(PI*i*j/n/48)
        NEXT i
        DRAW 12+2*j, 90+INT(z+1)
      NEXT j
      ENDPROC