Consider the hanging crane structure in Figure AP2.6. Write the equations of motion describing the motion of the cart and the payload. The mass of the cart is M, the mass of the payload is m, the massless rigid connector has length L, and the friction is modeled as Fb (t) = −bx(t) where x(t) is the distance traveled by the cart.

FIGURE AP2.6 (a) Hanging crane supporting the Space Shuttle Atlantis (photo courtesy of: NASA/ Jack Pfaller) and (b) schematic representation of the hanging crane structure. -x(t). p(t) F(t) L m u(t) (a) (b)