please give me a matlab code for this question. Code for duhamel equation especially response spectrum of D V A are needed.

1. Consider SDOF system with m-100 lbs.sec2/in, k-100 kipsin. D-0%, xo-xo-0. SDOF system is subjected to ground acceleration, xg(), given below. 386 2 4 6 t(se) (a) Evaluate time histories of relative displacement, relative velocity, and absolute acceleration, using Duhamel's integral, and determine the maximum responses of SDOF system. When initial condition is xofxo#0, Duhamel's integral becomes as follows: (b) For same system, evaluate the maximum responses for natural frequencies (o) of 10, 20 50 rad/sec, and plot spectra of displacement, velocity, and acceleration. 2. Response spectrum is obtained from the maximum responses of time histories of SDOF system for specific ground acceleration, natural frequency and damping. The maximum responses of SDOF system (relative displacement, relative velocity, absolute acceleration) can be defined as follows: S,D,)lmax ig (t) expl-wD(t -ind t-t')dt max max (a) Find a time history of ground acceleration for El Centro Earthquake (Imperial Valley Earthquake, El Centro, 1940. 4. 18, SO0E) from any digital sources. Obtain or write a program to evaluate the response spectrum for So, Sv, and SA. Plot displacement spectrum, velocity spectrum, and acceleration spectrum (Arithmetic plot) for D-3, 5, 10% (b) Plot response spectrum of El Centro earthquake in tripartite log paper four-way logarithmic plot) for D-3, 5, 10%. rmine maximum responses (displacement, velocity, acceleration) for a structure of D-5 and Th-1.0 sec using response spectrum obtained in step (a). For same structure, determire maximu m responses using response spectrum obtained in step (b). Explain what causes the difference in the results. 1. Consider SDOF system with m-100 lbs.sec2/in, k-100 kipsin. D-0%, xo-xo-0. SDOF system is subjected to ground acceleration, xg(), given below. 386 2 4 6 t(se) (a) Evaluate time histories of relative displacement, relative velocity, and absolute acceleration, using Duhamel's integral, and determine the maximum responses of SDOF system. When initial condition is xofxo#0, Duhamel's integral becomes as follows: (b) For same system, evaluate the maximum responses for natural frequencies (o) of 10, 20 50 rad/sec, and plot spectra of displacement, velocity, and acceleration. 2. Response spectrum is obtained from the maximum responses of time histories of SDOF system for specific ground acceleration, natural frequency and damping. The maximum responses of SDOF system (relative displacement, relative velocity, absolute acceleration) can be defined as follows: S,D,)lmax ig (t) expl-wD(t -ind t-t')dt max max (a) Find a time history of ground acceleration for El Centro Earthquake (Imperial Valley Earthquake, El Centro, 1940. 4. 18, SO0E) from any digital sources. Obtain or write a program to evaluate the response spectrum for So, Sv, and SA. Plot displacement spectrum, velocity spectrum, and acceleration spectrum (Arithmetic plot) for D-3, 5, 10% (b) Plot response spectrum of El Centro earthquake in tripartite log paper four-way logarithmic plot) for D-3, 5, 10%. rmine maximum responses (displacement, velocity, acceleration) for a structure of D-5 and Th-1.0 sec using response spectrum obtained in step (a). For same structure, determire maximu m responses using response spectrum obtained in step (b). Explain what causes the difference in the results