code: def update_c(self, fs=None, qinv=None, fc=None, kappa_c=1.0):
          
          detuning_term = self.freq**2 / (self.freq**2 - 1.0j *self.freq*fs * \
                                          qinv + fs**2)
          return self.c_res * kappa_c / (1 + 1.0j * self.freq/fc)*detuning_term
docs: Calculate the sensing function c(f,t) given the new parameters
          kappa_c(t), kappa_a(t), f_c(t), fs, and qinv.
  
          Parameters
          ----------
          fc : float
              Coupled-cavity (CC) pole at time t.
          kappa_c : float
              Scalar correction factor for sensing function at time t.
          fs : float
              Spring frequency for signal recycling cavity.
          qinv : float
              Inverse quality factor for signal recycling cavity.
  
          Returns
          -------
          c : numpy.array
              The new sensing function c(f,t).