Time-dependent damped harmonic oscillators
REVISTA BRASILEIRA DE ENSINO DE FISICA, (2013)Аннотация
In this work we analyze the solutions of the equations of motions of Lane-Emden oscillators, which are associated with a mass m(t) =
m(0)t(alpha), alpha > 0. These systems are damped harmonic oscillators with a time-dependent damping coefficient, gamma(t) = alpha/t We obtain analytical expression for x (t), (x) over dot(t) = v(t), e p(t) = m (t)(x) over dot for alpha = 2 and alpha = 4. We discuss the differences
between the expressions for the Hamiltonian and the mechanical energy
for time-dependent systems. We also compared our findings with the
results for the well-known Caldirola-Kanai oscillators.