We present an application of the Lagrangian variational method (LVM) to study the small-oscillation dynamics and ground-state properties of an interacting Bose gas in a one-dimensional dimple trap, for the first time. For this purpose, a Gaussian wavefunction ansatz—rich in variational parameters—is used for the analytical solutions of the equations of motion resulting from the LVM. The results of LVM are found to agree well with those due to the numerical Crank–Nicolson method. The strength of this method is shown to reveal details hidden in the wavefunction and its dynamics that are otherwise hard to obtain numerically or even experimentally. In this regard, the important role that the wavefunction-width plays in determining the properties of a trapped Bose gas is manifested. Via this method, the dependence of the breathing-mode frequency on the interactions, width of wavefunction, and dimple trap parameters, is demonstrated. A significant result is that in the ‘width-space’ of the wavefunction, the LVM yields a differential equation that describes the motion of a fictitious particle in an effective potential whose shape is by analogy similar to that of an interatomic interaction potential.