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PROGRAM PENDULUM
!
! Main Program for a driven pendulum under damping solved with
! the fourth-order Runge-Kutta algorithm.  
! Parameters: Q, B,and W (omega_0).  
!
     PARAMETER (N=1000,L=100,M=1)
     DIMENSION  Y(2,N)
         COMMON/CONST/Q,B,W
!
  PI = 4.0*ATAN(1.0)
  H  = 3.0*PI/L
  Q  = 0.5
  B  = 0.9
  W  = 2.0/3.0
  Y(1,1) = 0.0
  Y(2,1) = 2.0
!
! Using the Runge-Kutta algorithm to integrate the
! equation
!
  DO 100 I = 1, N-1
    T  = H*I
    Y1 = Y(1,I)
    Y2 = Y(2,I)
    DK11 = H*G1(Y1,Y2,T)
    DK21 = H*G2(Y1,Y2,T)
    DK12 = H*G1((Y1+DK11/2.0),(Y2+DK21/2.0),(T+H/2.0))
    DK22 = H*G2((Y1+DK11/2.0),(Y2+DK21/2.0),(T+H/2.0))
    DK13 = H*G1((Y1+DK12/2.0),(Y2+DK22/2.0),(T+H/2.0))
    DK23 = H*G2((Y1+DK12/2.0),(Y2+DK22/2.0),(T+H/2.0))
    DK14 = H*G1((Y1+DK13),(Y2+DK23),(T+H))
    DK24 = H*G2((Y1+DK13),(Y2+DK23),(T+H))
    Y(1,I+1) = Y(1,I)+(DK11+2.0*(DK12+DK13)+DK14)/6.0
    Y(2,I+1) = Y(2,I)+(DK21+2.0*(DK22+DK23)+DK24)/6.0
!
! Bring theta back to the region [-pi,pi]
!
    IF(ABS(Y(1,I+1)).GT.PI) THEN
       Y(1,I+1) = Y(1,I+1)-2.0*PI*ABS(Y(1,I+1))/Y(1,I+1)
        END IF
   100 CONTINUE
!
    WRITE(6,999)(Y(1,I),Y(2,I),I=1,N,M)
    STOP
  999 FORMAT (2F16.8)
     END
!
  FUNCTION G1 (Y1,Y2,T)
  COMMON /CONST/Q,B,W
       G1=Y2
  RETURN
  END
!
FUNCTION G2 (Y1,Y2,T)
COMMON /CONST/Q,B,W
  G2 = -Q*Y2-SIN(Y1)+B*COS(W*T)
RETURN
END
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