  We give an example of a simple mechanical system described by the generalized
harmonic oscillator equation, which is a basic model in discussion of the
adiabatic dynamics and geometric phase. This system is a linearized plane
pendulum with the slowly varying mass and length of string and the suspension
point moving at a slowly varying speed, the simplest system with broken
$T$-invariance. The paradoxical character of the presented results is that the
same Hamiltonian system, the generalized harmonic oscillator in our case, is
canonically equivalent to two different systems: the usual plane mathematical
pendulum and the damped harmonic oscillator. This once again supports the
important mathematical conclusion, not widely accepted in physical community,
of no difference between the dissipative and Hamiltonian 1D systems, which
stems from the Sonin theorem that any Newtonian second order differential
equation with a friction of general nature may be presented in the form of the
Lagrange equation.
