Refine the model of the motion of an undamped vertical spring to account for air friction, and include a graph of velocity.

a. Determine if changing any of the following affects the period; and if it does, determine a relationship between the parameter and the period: init_ displacement, mass, spring_constant.

b. How does changing spring_constant affect the graph of length?

c. Give the relationship between the length of the spring and its velocity. For example, when the velocity is zero, what is the position of the spring? At what stage(s) does the spring have a maximum velocity?