A simple beam AB is subjected to a distributed load of intensity q( ) x q 5 0 sin / px L, where 0 q is the maximum intensity of the load (see gure). Derive the equation of the deflection curve, and then determine the deflection max d at the midpoint of the beam. Use the fourth-order differential equation of the deflection curve (the load equation).

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?