The dynamic behavior of two adjacent single-degree-of-freedom structures connected with a friction damper is investigated under harmonic ground acceleration. The governing differential equations of motion of the coupled system are derived and solved for analytical harmonic response during the non-slip and slip motion in friction damper. The response of the coupled system under harmonic excitation is found to be periodic occurring in three different modes of vibration (i.e. stick-stick, stick-slip and slip-slip modes). The closed-form expressions in terms of system parameters and excitation were derived for necessary conditions to initiate the stick-stick and slip-slip modes. A parametric study is also conducted to study the influence of important system parameters on the response behavior of damper connected structures. The important parameters included are structure damping ratios, frequency ratio, mass ratio and damper slip force. It was observed that there exists an optimum slip force in the damper for which the peak displacement of a structure attains the minimum value. The friction damper with optimum slip force significantly reduces the dynamic response of the coupled structures. Finally, the influence of important parameters on the maximum displacement of friction damper is also investigated for its effective design in coupling the adjacent structures.