piston <- function(xx)
{
  ##########################################################################
  #
  # PISTON FUNCTION
  #
  # Authors: Sonja Surjanovic, Simon Fraser University
  #          Derek Bingham, Simon Fraser University
  # Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
  #
  # Copyright 2013. Derek Bingham, Simon Fraser University.
  #
  # THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
  # FOR THE USE OF THIS SOFTWARE.  If software is modified to produce
  # derivative works, such modified software should be clearly marked.
  # Additionally, this program is free software; you can redistribute it 
  # and/or modify it under the terms of the GNU General Public License as 
  # published by the Free Software Foundation; version 2.0 of the License. 
  # Accordingly, this program is distributed in the hope that it will be 
  # useful, but WITHOUT ANY WARRANTY; without even the implied warranty 
  # of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 
  # General Public License for more details.
  #
  # For function details and reference information, see:
  # http://www.sfu.ca/~ssurjano/
  #
  ##########################################################################
  #
  # OUTPUT AND INPUT:
  #
  # C = cycle time
  # xx = c(M, S, V0, k, P0, Ta, T0)
  #
  ##########################################################################
  
  M  <- xx[1]
  S  <- xx[2]
  V0 <- xx[3]
  k  <- xx[4]
  P0 <- xx[5]
  Ta <- xx[6]
  T0 <- xx[7]
  
  Aterm1 <- P0 * S
  Aterm2 <- 19.62 * M
  Aterm3 <- -k*V0 / S
  A <- Aterm1 + Aterm2 + Aterm3
  
  Vfact1 <- S / (2*k)
  Vfact2 <- sqrt(A^2 + 4*k*(P0*V0/T0)*Ta)
  V <- Vfact1 * (Vfact2 - A)
  
  fact1 <- M
  fact2 <- k + (S^2)*(P0*V0/T0)*(Ta/(V^2))
  
  C <- 2 * pi * sqrt(fact1/fact2)
  return(C)
}