%0 Journal Article %1 WOS:000329290400011 %A Aguiar, V %A Guedes, I %C CAIXA POSTAL 66328, 05315-970 SAO PAULO, BRAZIL %D 2013 %I SOC BRASILEIRA FISICA %J REVISTA BRASILEIRA DE ENSINO DE FISICA %K Frobenius' equation method; motion} of oscillators; {damped %N 4 %T Time-dependent damped harmonic oscillators %V 35 %X 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.

@article{WOS:000329290400011, abstract = {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.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {CAIXA POSTAL 66328, 05315-970 SAO PAULO, BRAZIL}, author = {Aguiar, V and Guedes, I}, biburl = {https://www.bibsonomy.org/bibtex/2d093f2eb36152eaf635f70f55965b6ca/ppgfis_ufc_br}, interhash = {34c2f0de81667c8601b6dc528c478b6d}, intrahash = {d093f2eb36152eaf635f70f55965b6ca}, issn = {1806-1117}, journal = {REVISTA BRASILEIRA DE ENSINO DE FISICA}, keywords = {Frobenius' equation method; motion} of oscillators; {damped}, number = 4, publisher = {SOC BRASILEIRA FISICA}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Time-dependent damped harmonic oscillators}, tppubtype = {article}, volume = 35, year = 2013 }