Dynamic response of discrete structural system can be well understood by acceleration measurement under free vibration. Sophisticated piezoelectric based accelerometers are employed for precise measurement of acceleration observed by the mass of the system to the dynamic excitation. However, displacement of the system is a key response parameter for determining internal forces and amplitude amplification of the dynamic system. These warrant double integration of acceleration signal measured for the system. First integration of acceleration signal gives velocity signal contaminated with ramp (slope) with respect to zero mean line due to presence of constant term of the integration affected by DC bias. Further integration to obtain displacement signal leads to polynomial divergence from zero mean line resulting in to error in numerical solution of discrete structural system. In the present study, a simple modified method of double integration is proposed to eliminate ramp and second order polynomial from velocity and displacement signals, respectively on integration of acceleration signal. The proposed algorithm uses band-pass filter multiple times on measured acceleration response of discrete structural system and truncates few initial data of filtered signals to arrive at the peak value. They are further integrated to have constant term of integration zero. The efficacy of the proposed method is established by correlating displacement response obtained through proposed algorithm with analytically obtained displacement response under free vibration with known initial conditions obtained from truncated measured signals for discrete single degree of freedom (SDOF) system at the laboratory. A good agreement with high order of co-efficient correlation, 0.99 is achieved for experimentally derived and doubly integrated displacement signal with that of analytically obtained displacement response of SDOF system.