# SECTION 4.9# Example 1de := m*diff(y(t),t,t) + b*diff(y(t),t) + k*y(t) = F0*cos(gamma*t);

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yp := A1*cos(gamma*t)+A2*sin(gamma*t);

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subs(y(t)=yp,de);

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expand(%);

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eq1 := -m*gamma^2*A1 + b*gamma*A2 + k*A1 = F0;

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eq2 := -m*gamma^2*A2 - b*gamma*A1 +k*A2 = 0;

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sol := solve({eq1,eq2},{A1,A2});

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A2 := rhs(sol[1]);

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A1 := rhs(sol[2]);

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yp;

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subs({m=10,k=49,b=3,F0=20,gamma=4},A1);

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A1_Ex1 := evalf(%);

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subs({m=10,k=49,b=3,F0=20,gamma=4},A2);

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A2_Ex1 := evalf(%);

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theta := arctan(A1_Ex1,A2_Ex1);

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A := sqrt(A1_Ex1^2 + A2_Ex1^2);

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yp_Ex1 := A*sin(4*t+theta);

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