I have one. A friend wishes to know the effect on the amplitude by adding three quarters on the top of a 77kg pendulum bob (the tower clock at the county building in Santa Barbara.*
The period change was quite obvious and measurable.** However, there was no detectable change in the amplitude. After some cogitation (I'm a bit slo these days.) I conclude that adding mass on the "down swing" will do nothing, but on the upswing will reduce the amplitude. I found the KE at BDC and concluded the energy to lift the quarters (~ 0.02kg) is so little the reduction in height, (h = L(1-cos(A)), is on the order of microns, and, therefore, not measurable by his method. [speed as measured by a photogate at BDC]
Here's my prob. Using the kinematic equations for constant acceleration etc. I fond the formula for speed at BDC (and the work-energy principle)
X dot = sqrt.(g*L) A as a means of measuring the amplitude.
I obtain the same formula by using the total energy of the P. using 0.5(M L^2 * theta dot) and m*g*h h = L(1-cos(theta) and using E = PE at the max deflection (amplitude). However, and this is my prob. To obtain the same equation I must use the approximation cos =~ 1 - theta^2 / 2!