9. Suppose we have a pendulum clock that uses a slightly damped oscillator to keep time. Suppose that the clock "ticks" cach time the pendulum am crosses 6 0, but the arm must reach a height of 6 = +0.1 to record the swing (that is, if the entire swing takes place with -0.1 < 6 < 0.1, then the clock doesn't tick). Suppose one tick is one second. In terms of the parameters b, m, and I, give a rough estimate of how long the clock can keep accurate time. Comment on why pendulum clocks must be wound.

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter3: Oscillations
Section: Chapter Questions
Problem 3.11P
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In Exercises 4-11, we consider the damped pendulum system
de
dt
ap
dt
b
sine
-v,
m
where b is the damping coefficient, m is the mass of the bob, I is the length of the arm,
and g is the acceleration of gravity (g 9.8 m/s?).
Transcribed Image Text:In Exercises 4-11, we consider the damped pendulum system de dt ap dt b sine -v, m where b is the damping coefficient, m is the mass of the bob, I is the length of the arm, and g is the acceleration of gravity (g 9.8 m/s?).
9. Suppose we have a pendulum clock that uses a slightly damped oscillator to keep
time. Suppose that the clock "ticks" each time the pendulum arm crosses e = 0, but
the arm must reach a height of 6 = +0.1 to record the swing (that is, if the entire
swing takes place with -0.1 < 6 < 0.1, then the clock doesn't tick). Suppose one
tick is one second. In terms of the parameters b, m, and I, give a rough estimate of
how long the clock can keep accurate time. Comment on why pendulum clocks must
be wound.
Transcribed Image Text:9. Suppose we have a pendulum clock that uses a slightly damped oscillator to keep time. Suppose that the clock "ticks" each time the pendulum arm crosses e = 0, but the arm must reach a height of 6 = +0.1 to record the swing (that is, if the entire swing takes place with -0.1 < 6 < 0.1, then the clock doesn't tick). Suppose one tick is one second. In terms of the parameters b, m, and I, give a rough estimate of how long the clock can keep accurate time. Comment on why pendulum clocks must be wound.
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