Many researchers have recently reported work on the oscillatory response of premixed flames in the framework of the unsteady G-equation, with the flame transfer function defined in terms of the flame-area fluctuations. Many of these works assume, contrary to experimental observations, that (a) the flame speed is constant, (b) the flame responds harmonically to input velocity fluctuations, and (c) the base of the flame where it is anchored on the burner rim is always fixed during the oscillations. The present work relaxes these assumptions in the linear framework analytically, and with nonlinearity, computationally. The flame speed is considered to vary due to the unsteady curvature in the flame shape. It is found that, with the constant flame speed, the disturbance propagating along the shoulder of the flame oscillates at a different frequency than that imposed; but with variable flame speed, the amplitude of this perturbation decays with time. The response at the excitation frequency is not affected by the curvature effect on the flame speed except at very high frequencies atypical of oscillations encountered during combustion instability in practical combustors.