Consider two identical, coupled oscillators (as in Figure 12-1). Let each of the oscillators be damped, and let each have the same damping parameter β. A force F0 cos wt is applied to m1. Write down the pair of coupled differential equation that describes the motion. Obtain the solution by expressing the differential equations in terms of the normal coordinates given by Equation 12.11 and by comparing these equations with Equation 3.53. Show that the normal coordinates η1 and η2 exhibit resonance peaks at the characteristic frequencies w1 and w2, respectively.