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  • %Initial condition response of mass-spring systemm=1; %massc=0; %damping constantk=1; %stiffnessnum=[1]; %numerator of transfer-function model for M-K systemden=[m 0 k]; %denominator of transfer-function model for M-K systemsys_tf=tf(num,den); %build a transfer-function systemsys_ss=ss(sys_tf); %obtain a state-space system model%Investigate the state-space model of M-K system to determine%which state variables correspond to position/velocityx0=[5 2]'; %specify initial condition for M-K systemtime=[0:0.05:20]; %specify time vector for simulation%simulate M-K system for initial condition response[Y,T,X]=initial(sys_ss,x0,time);plot(T,Y)%Initial condition response of mass-spring-damper systemm1=1;k1=1;zeta1=0.1; %under-damped system damping ratio.wn1=sqrt(k1/m1); %undamped natural frequencyc1=2*m1*zeta1*wn1; %damping constantnum1=[1];den1=[m1 c1 k1];sys_tf1=tf(num1,den1);sys_ss1=ss(sys_tf1);x01=[5 2]';time1=[0:0.05:20];[Y1,T1,X1]=initial(sys_ss1,x01,time1);plot(T1,Y1)