a. Suggest a method of solving the fourth-order differential equations derived in Problem 5.79 (in terms of

Question:

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):-