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Xâ€(t)+X(t)=0 X(0)=1 X’(0)=0 X(t)=cost X(t)=Acos(wt)+Bsin(wt) =>X(t)=Acos(t)+Bsin(t) =>X’(t)=-Asin(t)+Bcos(t) X(0)=Acos(0)=1=>A=1 X’(0)=Bcos(0)=0=>B=0 X(t)=cos(t).
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X”(t)+X(t)=0 X(0)=1 X’(0)=0 X(t)=cost X(t)=Acos(wt)+Bsin(wt)=>X(t)=Acos(t)+Bsin(t) =>X’(t)=-Asin(t)+Bcos(t) X(0)=Acos(0)=1=>A=1 X’(0)=Bcos(0)=0=>B=0X(t)=cos(t)