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Step 3The Pendulum
Pendulums are an interesting mechanism. They are a weight at the end of a string or pole, with a pivot at the opposite end of the weight. The period of a pendulum is the time it takes to go from one side to the other and back again. The neat thing about pendulums is that this time, or period, is not dependent on the amount of weight or length of arc, it's dependent on the length of the pendulum. So, if you had a 2 foot long pendulum with a 5 pound weight, pulled to the right at 90 degrees, it would take the same amount of time to swing across and back as a 2 foot long pendulum with 2 pounds of weight pulled to the right at 30 degrees. The weight at the end of the pendulum does affect how many times the pendulum will swing. So the pendulum with the 5 pound weight will swing for a longer amount of time, than the 2 pound weight. This is helpful because we want to keep the pendulum swinging. You can, however, have too much weight. As we will see next, the escapement helps give the pendulum a push. If you have too heavy of a weight, you will not have enough energy to keep it swinging.
For our clock, we want to have a period of 2 seconds. That way, it will take the pendulum 1 second to swing to one side. With each swing the escapement will allow the escape gear to turn one tooth at a time. If the period is 2 seconds, this will basically make the escape gear our second hand since it is rotating one tooth every second. For a period of 2 seconds we need it to have a length of 1 meter. Since our escape lever will have 2 teeth, one to stop the escape gear at each end of the pendulum swing, our pendulum will need to have 30 teeth. It will make one rotation every 60 seconds. Many pendulum clocks have the escape gear on the second hand axle. That is what we are going to do.
As the pendulum swings back and forth, it rotates the escape lever in and out of the escape gear. This causes the clock gears to stop and start rotating every second. The lever is designed so that as it is moving out of the escape gear, the gear gives it a little push. This push is enough to keep the pendulum swinging.
For our clock, we want to have a period of 2 seconds. That way, it will take the pendulum 1 second to swing to one side. With each swing the escapement will allow the escape gear to turn one tooth at a time. If the period is 2 seconds, this will basically make the escape gear our second hand since it is rotating one tooth every second. For a period of 2 seconds we need it to have a length of 1 meter. Since our escape lever will have 2 teeth, one to stop the escape gear at each end of the pendulum swing, our pendulum will need to have 30 teeth. It will make one rotation every 60 seconds. Many pendulum clocks have the escape gear on the second hand axle. That is what we are going to do.
As the pendulum swings back and forth, it rotates the escape lever in and out of the escape gear. This causes the clock gears to stop and start rotating every second. The lever is designed so that as it is moving out of the escape gear, the gear gives it a little push. This push is enough to keep the pendulum swinging.
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Please reread the teachings of Galileo Galilei. It's Physics 101.
Since Galileo discovered the isochronic property of the pendulum, they have been the world's most accurate timekeeping technology until the 1930s. This could NOT be so if the angle of the swing would vary the frequency.
Wider swings do NOT take longer, unless you are comparing a swing of 1 degree v. 179 degrees. Then, the variation in period or frequency is really influenced more by friction in the bearing and air friction.
Clocks, use relatively low angle pendulum swings, so these factors are kept at a minimum as there is less movement. The only reason a clock's pendulum may have a higher mass, is to take advantage of Newton's First Law of Motion to overcome as much of the friction to keep it moving as long as posible. The addition, or subtraction of mass will NOT change the frequency of the pendulum.
The period of swing of a simple gravity pendulum depends on its length, the local strength of gravity, and to a small extent on the maximum angle that the pendulum swings away from vertical, called the amplitude.
It is independent of the mass of the bob.
If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is a function of the length of the pendulum and gravity.
For small swings, the period of swing is approximately the same for different size swings: that is, the period is independent of amplitude.
This property, called isochronism, is the reason pendulums are so useful for timekeeping.
Successive swings of the pendulum, even if changing in amplitude, take the same amount of time.
http://en.wikipedia.org/wiki/Christiaan_Huygens
For small swings, the effect is quite small and could be ignored in a weight driven clock, whose pendulum swings are reasonably constant and therefore unvarying. For spring driven clocks, where the swing gets smaller and smaller as the spring unwinds, the effect was bad enough that a fusee was added to the finest movements to keep the driving force, and therefore pendulum swing, as constant as possible. Cheaper spring driven clocks weren't very accurate anyway, and the recoil escapement used in those movements tended to drive the pendulum faster when wound tight, which partially compensated for the wider (slower) swings of the pendulum. Not that it really mattered in that era, as people set their clocks daily anyway, to a sundial or the town clock bell.....
Cheers,
Chris
"The frequency of the pendulum is dependent on the length of the string or wire. The shorter the wire, the greater the frequency or how fast it goes back and forth.
The frequency is independent of the amplitude of the swing, provided the initial angle is not large. At larger angles, there is a slight change in the frequency.
Also, the frequency is independent of the mass of the bob. In other words a pendulum with a heavy bob will move at the same rate as one with a lighter weight bob. But this only makes sense, since the acceleration of gravity on a falling object is independent of the mass of the object."
See:
http://www.school-for-champions.com/science/pendulum.htm