Problem $2\mathrm{.}5$

Find the equivalent system with respect to the angle of the crank for the petroleum pump shown below. The oil well acts like a spring with a spring constant of $45\mathrm{.}0M\frac{N}{m}.$ The piston has a mass of $26$ kg $.$ The horsehead has a mass of $125$ kg $.$ The rigid walking beam has a mass of $60$ kg and a mass moment of inertia of $354kg*m^2$ about the pivot point on the stationary frame. $l_2=3m,l_3=4m,$ and $l_4=6m.$ Assume the rigid link between point $B$ and the crank stays approximately vertical at all times. It has a mass of $54$ kg $.$ The crank has a mass of $13$ kg and a mass moment of inertia of $2\mathrm{.}1kg*m^2$ about its center of rotation. It has a radius of $30$ cm $.$ The crank shaft is a solid tube of steel $(E=200$GPa,$G=79$GPa$)$ with a diameter of $3$ cm $,$ a length of $9$ cm $,$ and a damping constant of $28N*m*\frac{s}{r}ad.$ Assume that the shaft can twist but not bend. Assume the other end of the shaft is connected to a motor, and that the motor can be treated as fixed.

Answer: $34\mathrm{.}7kg*m^2,7\mathrm{.}27MN*\frac{m}{r}ad,28N*m*\frac{s}{r}ad$