Exercise 4.3.7 Consider a vibration isolation table as modeled in Example 4.2 and the ODE (4.9). Suppose that the mass of the tabletop is m = 100 kg, at a nominal height of Lo = 1 meter, and the isolation leg has spring constant k = 10# newtons per meter and damping constant c = 2000 newtons per meter second. Use g = 9.8 meters per second squared. Let y(t) denote the height of the table as a function of time. (a) Find the position y(t) = yeq of the table if only gravity acts on the tabletop (and d(t) = 0). (b) Suppose the ground begins to vibrate according to d(t) = 10-cos(40mt) (20 hertz) at time t = 0. If the table has initial data y(0) = yeq and y'(0) = 0, find the motion y(t) of the table. Plot y(t) for 0 1? How does this compare to the amplitude of d(t)? Does the table effectively dampen this motion? (c) Consider an alternate scenario in which d(t) = 0 and the table is at its equilibrium position y(t) = yeq fort