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The 5kg mass is pulled by two forces, gravity and the arbitrary force ’F’. These forces are described in vector form, with the positive ’z’ axis pointing upwards. To find the equations of motion the forces are summed. To eliminate the second derivative on the inertia term the equation is integrated twice. The result is a set of three vector equations that describe the x, y and z components of the motion. Notice that the units have been carried through these calculations. 9 Assume we have a mass that is acted upon by gravity and a second constant force vector.

Where the mechanism has been broken the contact forces must be added to both of the separated pieces. 28. At joint A the forces are written as two components in the x and y directions. For joint B the force components with equal magnitudes but opposite directions are added to both FBDs. 28 Note: Don’t forget that forces on connected FBDs should have equal magnitudes, but opposite directions. 3 SYSTEM EXAMPLES An orderly approach to system analysis can simplify the process of analyzing large systems.

In this case the force and displacement are both compressive. The force is calculated by multiplying the damping coefficient by the velocity, or first derivative of position. Aside from the use of the first derivative of position, the analysis of dampers in systems is similar to that of springs. 19 x Kd d F = K d  ----- x dt F (15) Aside: The symbol shown is typically used for dampers. It is based on an old damper design called a dashpot. It was constructed using a small piston inside a larger pot filled with oil.