This is the Free-body diagaram of our system. What the Free-body diagram helps us determine is forces and the directions of those forces in the system.

In our system, we have 4 total forces:

The Spring Force or dampening force, caused by the bungee cord;

The Frictional Force caused by the air resistance;

The inertial force of the mass, the mass being the person. The direction is opposite the motion of the mass

The gravitational force;

We have our translational system, in whcih the mass is in motion with Velocity (V). The mass has displacement (X) from it's intial position and it's final position.

The Sprig Force comes from the Stiffness in the Cord, and is equal to the Spring Constanst ( K ) mulitplied by the displacement of the mass.

Hence-it's equal to KX

The frictional force comes from the air resistance and is equal to the friction Coeffecient (B) multiplied by the Velocity. Velocity is the same as the 1st derivative of the displacement ( X ' ).

Hence-it's equal to BX'

The inertial force oppoes the motion and is equal to the Mass multiplied by the acceleration of the mass. Acceleration is the same as the 2md derivative of the displacement ( X'' ).

Hence-it's equal to MX''

There is also the gravity acting on the system. That is equal to the mass multiplied by the gravitational constant g=9.82 m/s^2.

Hence-it's equal to Mg