<p>This article offers complete analytical solutions to the one-dimensional time-dependent Schrödinger equation for an explicit frequency-dependent factor with time-varying mass and frequency by implementing the Lewis-Riesenfeld (LR) dynamical invariance procedure. The present approach proposes a dynamically quantum-invariant phase factor for the wave function of the time-dependent harmonic oscillator model. In this context, a time-dependent system is often transformed into a time-independent one via an integral of motion under appropriate unitary transformations. Various cases of oscillatory systems involving time-dependent mass and frequency forms are also examined algebraically. As a result, the corresponding analytical solutions of the Pinney equation can be employed in nonlinear configuration analyses of such systems.</p>