Digital Assignment- MAT2002 AODE By method of undetermined coefficients: 1 Solve the initial-value problem y" + y = 4x + 10 sin x, y(TT) = 0, y'(7) = 2. 2 A vibrational system consisting of mass (m = ; slug or kilogram) attached to a spring (k =2 1b/ft or N/m). The mass is released from rest 2 unit (foot or meter) below the equilibrium position. The motion is damped (B =1.2) and is being driven by an external periodic (T =7/2 s) force beginning att =0. Intuitively we would expect that even with damping, the system would remain in motion until such time as the forcing function was "turned off," in which case the amplitudes would diminish. However, as the problem is given, f(t) =5 cos 4t will remain "on" forever. Using Method of variation of parameters 3 3y" - by' + 6y = et sec x 41" - 2y'ty= ex 1 + x2 Solve by Matrix Method 5 The system of differential equations for the currents i, (t) and i2(t) in the electrical network shown in FIGURE 10.4.3 is dt - (R1 + R2)/L2 R2/ L2 R2/ L1 -R2/ LI ( 13 ) + ( FIZZ ). Use variation of parameters to solve the system if R, = 8 0, R2 = 3 0, L, = 1 h, L2 = 1 h, E(t) = 100 sin t V, i, (0) = 0, and i2(0) = 0. M i1 R1 E L1 SR2 00000 L2 FIGURE 10.4.3 Network in Problem 35