You are trying to match that design spectrum too closely. An effect of this (in the frequency domain) is most clearly demonstrated by the step in the Fourier spectrum at ~20 seconds. But that is just one visually obvious symptom of the more pervasive problem. Real earthquake motions will never match that idealized design spectrum as closely as what you have done. Real earthquake motions are lumpy and messy. You need to think of that idealized design spectrum as more of a threshold that encompasses the range of possible actual earthquake motions.

For example, see https://www.sciencedirect.com/book/9781845695187/structural-dynamics-of-earthquake-engineering "17.15 Distinction between design and response spectra

A design spectrum conceptually differs from a response spectrum in two ways. A response spectrum is a jagged plot of peak response of all possible SDOF systems, and hence is a description of a particular ground motion. A design spectrum is smooth and is the envelope of the different elastic design spectra. Figure 17.27 shows a design spectrum as the envelope of design spectra for earthquakes originating on the different faults. The conceptual differences between the response obtained from the response spectrum and design spectrum are demonstrated in Fig. 17.27. In this figure, notice that for some periods these values obtained for response and design spectra are the same, and for some other periods there is a considerable discrepancy. In general, the response spectrum and the design spectrum do not yield the same result since the former represents the response to a specific earthquake, while the latter represents only the predicted response to an earthquake having the same PGA (peak ground acceleration)." One can see the figure 17.27 referred to in the excerpt here: https://www.sciencedirect.com/topics/engineering/design-spectrum

Matthew Mabey, the output I obtained was based on 10 number of iterations. The perfect matching at the beginning is because I have used a time step of 0.05 for the natural period of structure. Because my solution of response spectra became erroneous at lesser period. However I am again trying to draw response spectra following the Newmark average acceleration method which is stable for any time step. In mean time I just wanted to know how do we correct the drift in velocity and displacement which is imminent due to the spectral matching procedure ???

Thanks.