Simple Harmonic Motion: Maximum Speed of a Grandfather Clock Pendulum in cm/s

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SUMMARY

The maximum speed of a grandfather clock pendulum, which swings with an amplitude of 22.0 mm and a period of 1.00 s, can be calculated using two methods. The first method, based on simple harmonic motion (SHM), yields a maximum speed of 6.91 cm/s. However, this value is incorrect according to the discussion. The second method involves energy conservation principles, assuming gravitational acceleration (g) of 9.81 m/s², which also needs to be explored for accurate results.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Knowledge of energy conservation principles in physics
  • Familiarity with pendulum mechanics
  • Basic mathematical skills for calculations involving trigonometric functions
NEXT STEPS
  • Calculate maximum speed using energy conservation principles in pendulum motion
  • Review the derivation of maximum speed in SHM
  • Explore the effects of varying amplitude on pendulum speed
  • Investigate the relationship between period and maximum speed in pendulums
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Physics students, educators, and anyone interested in the mechanics of pendulums and simple harmonic motion.

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Homework Statement


A grandfather clock is constructed so that it has a simple pendulum that swings from one side to the other, a distance of 22.0 mm, in 1.00 s. What is the maximum speed of the pendulum bob? Use two different methods. First, assume SHM and use the relationship between amplitude and maximum speed.
First answer to be in cm/s

Second, use energy conservation. Assume g = 9.81 m/s2
Second answer to be in cm/s


The Attempt at a Solution


The amplitude is (22.0 mm)/ 2 = 11.0 mm and the period is 1.00 s.
1st method:
(2*pi*11*10^-3 m) / 1 s = 6.91 cm/s
6.91 isn't showing as the correct answer, wondering what i did wrong.
 
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Period is the time for one to and fro motion of the pendulum.
 

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