In this work we study a coupled system of two classical oscillators with time-dependent masses (m i), spring constants (k i) and coupling parameter (κ). To obtain the solution of the equation of motion for each oscillator, we use a canonical transformation to rewrite the Hamiltonian of the coupled system as the sum of the hamiltonians of two uncoupled harmonic oscillators with modified frequencies and unitary masses. We analyze the behavior of x i,v i = ẋi and the phase diagram x i vs. v i for the system m1=m2=moeγt and k1=k2=κ=koeγt
coupled oscillators; canonical transformation
