Re: [Phys-l] real-world mechanics problem

[John Mallinckrodt <ajm@csupomona.edu>]

Bernard Cleyet wrote:

> 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] ...

Beyond the fact that I can't find any data with enough information to make any use of, it seems to me that you are barking up the wrong tree to try to relate the period change to an amplitude change that depends on where in the cycle you add the quarters.  (If I read correctly between the lines, you seem to be treating this as an inelastic collision between the pendulum and initially motionless quarters with an energy loss occurring if the pendulum happens to be moving.)

First of all, the drive mechanism will presumably act to counter any amplitude change that might result from whatever mechanical disturbance might occur during the quarter placement.

Second, the period change from adding quarters will likely have more to do with the change in the relative mass distribution (e.g. altering the radius of gyration) than any change in amplitude.

John Mallinckrodt
Cal Poly Pomona