The state equation of a second order system is
$$x(t) = Ax(t),\,\,\,\,x(0)$$ is the initial condition.
Suppose $$\lambda_1$$ and $$\lambda_2$$ are two distinct eigenvalues of A and $$v_1$$ and $$v_2$$ are the corresponding eigenvectors. For constants $$\alpha_1$$ and $$\alpha_2$$, the solution, $$x(t)$$, of the state equation is
- A$$\sum\limits_{i = 1}^2 {{\alpha _i}{e^{{\lambda _i}t}}{v_i}} $$
- B$$\sum\limits_{i = 1}^2 {{\alpha _i}{e^{2{\lambda _i}t}}{v_i}} $$
- C$$\sum\limits_{i = 1}^2 {{\alpha _i}{e^{3{\lambda _i}t}}{v_i}} $$
- D$$\sum\limits_{i = 1}^2 {{\alpha _i}{e^{4{\lambda _i}t}}{v_i}} $$
✓ Correct answer: A
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