The primary objective of this paper is to analyze the synchronization phenomena in a coupled friction-induced oscillator consisting of two cantilever beams with tip-masses subjected to base excitations. The coupling is achieved by connecting a linear spring between the tip-masses, which are in frictional contact with a rigid rotating disk. The Pearson time correlation coefficient is used to measure the strength and mode of synchronization between the oscillations of the coupled system. Periodicity of the motions is determined by evaluating the Poincaré map wherein the zero velocity crossing from positive to negative is considered as the Poincaré section. The fundamental frequency of the coupled motion and its harmonics are obtained from the Fast Fourier Transform (FFT) of the time responses. A bifurcation study is conducted to identify the periodicity of motion of both the uncoupled and coupled systems. The coupled system is found to be synchronized for the single-periodic, multiperiodic, and quasi-periodic motions, but not for chaotic motions. Multiple basins of attractions of initial conditions corresponding to different synchronization characteristics are observed. The coupled system shows a large dependence of the mass ratio detuning factor (MRDF) on the synchronization characteristics; in-phase synchronization is obtained for smaller MRDF, which eventually becomes out-of-phase for larger MRDF. A special study conducted confirms that the coupling can be used to control the amplitude as well as the stick-phase of motion in friction oscillators.