How does the mass of a string affect the period of a pendulum?

[ptrainerjoe]

How would the period of a pendulum change if A)the string's mass was negligible and b) the stings mass had to be accounted for. I can think of arguments for both but can't find an equation or definite answer for either one.
I think the period will increase since I=I(string)+ml^2 and the period equals T=2pi*sqrt(I/mgl)
Help please!

 

[HallsofIvy]

If the string's mass was not negligible, in comparison to the "bob", where would the center of mass be? How does the period depend upon the length of a pendulum?

 

[Doc Al]

The period of a physical pendulum is given by:
$$T = 2 \pi \sqrt{I/mgl_{cm}}$$
If we include the mass of the string: I increases, of course, but so does m; but the length (from pivot to center of mass) decreases. To find out which effect dominates, you'll have to plug in expressions for I, m, and l and then compare the period to that of a simple pendulum without the string's mass.

According to my analysis (do it for yourself), if you include the mass of the string, the period would slightly decrease.