申論題

1. Consider the two-mass system in Figure I, where k₁ and k₂ are spring constants; x₁ and x₂ are displacements of m₁ and m₂, assuming that both springs have their natural lengths when x₁ = x₂ = 0. The surface is frictionless and f is an external force applied to m_1.

(a)  Choose x₁ as the output of the system. Write down the state space representation using as the state vector, where denotes the time derivative of for i = 1,2.