When a ring is threaded on an elastic string which is attached to the ceiling at two points, then ignoring friction, the particle will come to equilibrium at the midpoint of the string and the tension will be the same throughout the string. Suppose the modulus of elasticity of the string is
and the natural length of the string is
The length of the string with the ring attached is
The tension in the string is then
Resolving vertically gives
In general we can measure
then find
by writing
oris given, then
can be found using a numerical method.