The time-dependent step-down and step-up operators a(t) and a(dagger)(t) for the linearly forced Morse oscillator are constructed assuming a general time-dependent potential. The time evolution of the solutions to the time-dependent Schrodinger equation is shown to be governed by a second-order differential equation analogous to that appropriate for a harmonic oscillator with a time-dependent farce constant. Using a periodic forcing potential, the condition for parametric resonance is investigated. This mathematical model can describe the dissociation of a chemical bond.