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In this book we have considered the well known time- dependent harmonic oscillator under the action of external driving force. We introduced two models for the time-dependent mass; an alternative model of the damped harmonic oscillator as well as the pulsating harmonic oscillator. The wave function in the number and in the coherent states besides the Green's function for both models are obtained. For the pulsating oscillator model we have obtained asymptotic solution near resonance besides the solution of the equations of motion using the perturbation method. Furthermore we have considered the constants of motion for the first model where we obtained two classes of the linear and quadratic invariants besides an application of su(1,1) Casimir operators. Also we have examined the nonclassical properties concentrating on the squeezing phenomenon in addition to the sup-Poissonian and super Poissonian phenomena.