# Period of interrupted pendulum

1. Oct 5, 2015

### Bob Jagnaf

An interrupted pendulum is one in which the string strikes a rod directly below the pivot point causing the pendulum bob to deviate from its previous circular trajectory into a trajectory of a smaller radius. Depending on the original angle of displacement θ and where the rod is placed relative to the total length of the string, the bob may or may not wind itself completely around the rod.

Calculate the minimum distance x in terms of L and θ that will cause the pendulum bob to completely wrap around the rod. You should be careful here – the bob must have sufficient energy to completely circle the rod, and not enter a projectile motion pattern of free fall.

Any solutions is appreciated, steps to solutions are very valuable. Thanks!

1. The problem statement, all variables and given/known data

L= total length of string to center of mass from the inital point of the pendulum.

2. Relevant equations

I found the period of a interrupted pendulum. That is all I have.

3. The attempt at a solution

I am totally lost on how to do this. Can anyone guide me?

2. Oct 5, 2015

### haruspex

It is not enough to say you are completely lost. You must have done some previous work with pendulums, so should have some expressible thoughts.
I'll give you this tip: think of it as two separate phases.
In the first, the pendulum is swinging down towards the rod. Since the rod has not been reached, it plays no part. What equation describes this phase?
In the second, it has reached the rod and is starting to rotate about it. What part of the set up can be ignored in this phase?