Example In the configuration in Fig.5.1.1,the first spring is stretched x units and the second by y-x units.We apply Newton's law of motion to the two "free body diagrams"shown in Fig.5.1.2;we thereby obtain the system m1x”=-k1x+k20y-) (1) m2y”=-k20y-x)+ft) of differential equations that the position function x(t)and y(t) must satisfy. 4口10,1至，1无13000 Linear of Differential EquationsExample In the configuration in Fig.5.1.1, the first spring is stretched x units and the second by y−x units. We apply Newton’s law of motion to the two “free body diagrams” shown in Fig.5.1.2; we thereby obtain the system m1x 00 = −k1x+k2(y−x) (1) m2y 00 = −k2(y−x) +f(t) of differential equations that the position function x(t) and y(t) must satisfy. For instance, if m1 = 2,m2 = 1, k1 = 4, k2 = 2, and f(t) = 40 sin 3t in appropriate physical units, then the system in (1) reduces to 2x 00 = −6x+2y (2) y 00 = 2x−2y+40 sin 3t. Linear Systems of Differential Equations