Some　perturbation　methods　in　the　studying　vibrations　of　the　linear　time-varying　(LTV)　system　are　discussed.　Three　classical　perturbation　methods,　namely,　averaging　method,　harmonic　balance　method,　and　multiple　scales　method　with　linear　scales,　have　been　used　from　a　new　perspective　based　on　analytical　approximations　to　the　corresponding　LTV　ordinary　differential　equations.　The　deploying　beam　model　has　been　taken　as　an　example　to　validate　the　explicit　approximate　solutions　obtained　by　these　perturbation　methods.　It　is　demonstrated　that　such　approximate　solutions　have　good　agreement　with　numerical　and　exact　solutions,　excluding　the　vicinity　of　the　turning　point.