Resonances in a Clock

I have a grandfather clock that has a fairly light pendulum. There are three relatively heavy weights that drive the clock. When the weights get down near the pendulum, the swinging of the pendulum causes the weights to swing also.If I align the weights all in a row instead of staggered, the pendulum will stop when it gets to the weights. The pendulum never touches the weights. What gives?
- David (age 69)
Cedar Park, TX, USA

That's a very nifty problem. Here's some thoughts.

When the weights get down near the pendulum they form their own pendulums which have an oscillation period close to that of the main pendulum. When you have two oscillators with closely matched periods even a weak coupling between the oscillators causes energy to gradually shift back and forth between them. You can model this to see for yourself by making two pendulums from weights on strings and tying the strings to a slightly wobbly support. Compare what happens after you start one pendulum going in the case where the string lengths are about equal and cases where they aren't. I think you'll find that only for matched lengths the energy starts in one pendulum, goes to the other, then comes back, etc. Meanwhile the energy gradually dribbles away via friction.

In your clock there's some apparatus to trickle energy back into the pendulum to keep it swinging despite frictional loss. (The weights supply that energy, as you noted.) If the pendulum quits swinging, however, that apparatus doesn't get it started again. So if the energy flows from the main pendulum to the lined-up weight pendulum, that apparatus shuts down and it looks like not enough energy gets back to restart the main pendulum.

If the three weights are not lined up, the effects of the three weight pendulums on the main one are out of phase with each other. If you think of lots of things pushing and pulling out of phase, the effect tends to cancel. So I guess that's why with the three weights out of phase the main pendulum isn't affected that much.

Mike W.

 

(published on 04/21/2016)