The blogger claims no originality of his problem below.
A ball of mass 
is being passed through a smooth extensible light string, the two ends of which being attached to walls a distance 
apart.
When time 
:
when 
:
when 
:
when 
:
when 
:
when 
:
when 
:
such that stroboscopically for ![t\in [t_0,t_6]](https://physicspupil.com/wp-content/ql-cache/quicklatex.com-38671012185926e19155559d6237fe4e_l3.svg "Rendered by QuickLaTeX.com")
, we see the ball’s trajectory fits into a parabola as can be described by some quadratic equation:
The tension 
of the string and the speed 
of the ball are time-varying variables dependent on mass and distance as well. By considering the free-body diagrams of the ball and of the string in discrete time frames 
‘s (where 
), find the equation of motion at continuous time intervals of 
.
This problem is not to be attempted.