a. Suggest a method of solving the fourth-order differential equations derived in Problem 5.79 (in terms of \(x_{1}(t)\) or \(x_{2}(t)\) ).

b. How can we apply the known initial conditions \(x_{1}(0), x_{2}(0), \dot{x}_{1}(0)\) and \(\dot{x}_{2}(0)\) while solving the fourth-order differential equation in terms of \(x_{1}(t)\) ?

Data From Problem 5.79:-

Derive the fourth-order differential equations of motion of the two-degree-of-freedom system shown in Fig. 5.5 (a) in terms of \(x_{1}(t)\) and \(x_{2}(t)\) separately.

Figure 5.5(a):-

k m -fi(t) (1)x- k 00000 (a) m2 (1)x- 2(t) k3 Cz