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In Exercises 4-11, we consider the damped pendulum system de dt ap dt 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/s²).

In Exercises 4-11, we consider the damped pendulum system de dt ap dt 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/s²).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve both parts properly

6. Suppose we have a pendulum clock that uses only a slightly damped pendulum to keep time. The clock "ticks" each time the pendulum arm crosses e = 0. (a) As the clock "winds down" (so the amplitude of the swings decreases), does the clock run slower or faster? (b) If the initial push of the pendulum is large so that the pendulum swings very close to the vertical, will the clock run too fast or too slow?
Transcribed Image Text:6. Suppose we have a pendulum clock that uses only a slightly damped pendulum to keep time. The clock "ticks" each time the pendulum arm crosses e = 0. (a) As the clock "winds down" (so the amplitude of the swings decreases), does the clock run slower or faster? (b) If the initial push of the pendulum is large so that the pendulum swings very close to the vertical, will the clock run too fast or too slow?
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?).
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