The model of the mechanical system in Figure A.4 (no friction, no damping) is governed by \left\{\begin{array}{l} m_{1} y_{1}^{\prime \prime}=-k_{1} y_{1}+k_{2}\left(y_{2}-y_{1}\right) \\ m_{2} y_{2}^{\prime \prime}=-k_{2}\left(y_{2}-y_{1}\right)-k_{3} y_{2} \end{array}\right. Let m1 =

m2 = 10 kg, k = k3 = 20 kg/sec?, k2 = 40 kg/sec2. Find the solution satisfying the initial conditions y1(0) = y2 (0) = 0, y(0) = 1 m/sec, y(0) = -1m/sec.