Simple Harmonic Motion: Pendulum of Clock Replaced by Spring-Mass

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SUMMARY

The discussion centers on calculating the mass required for a spring-mass system to match the period of a pendulum clock. The spring constant is given as 0.1 N/m, and the initial calculation incorrectly concluded that the mass should be 25 grams. However, upon realizing that the period of the pendulum clock is actually 2 seconds, the correct mass is determined to be 10 grams. The error stemmed from an incorrect assumption about the period of oscillation.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with the formula for the period of a spring-mass system
  • Knowledge of spring constants and their units
  • Basic algebra for solving equations
NEXT STEPS
  • Review the derivation of the period formula T=2π(m/k)^(1/2)
  • Study the differences between pendulum motion and spring-mass systems
  • Explore the effects of varying spring constants on oscillation periods
  • Practice problems involving mass-spring systems and their oscillation periods
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to simple harmonic motion.

hermy
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Homework Statement



The pendulum of a clock is replaced by a spring-mass system with the spring having spring constant 0.1 N/m. What mass should be attached to the spring?


Homework Equations



T=2 pi (m/k)1/2

The Attempt at a Solution



1 = 2 pi (m/0.1)1/2
1 = 4 pi2 m/0.1

solving this, m= 25 grams

The answer is supposed to be 10 grams. What is wrong in my solution?

Thanks for the help.
 
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hermy said:
1 = 2 pi (m/0.1)1/2
1 = 4 pi2 m/0.1

solving this, m= 25 grams
You're off by a factor of 10.

The answer is supposed to be 10 grams. What is wrong in my solution?
You are assuming that the period is 1 second. Was that specified in the problem? (Was information given about the pendulum?)
 
I'm sorry, this question turned out to be quite easy. I came to know that the time period of a pendulum clock is 2s. Putting all this together, the answer does come out. Thanks for the help.
 

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