Simple Pendulum & Elevator Homework | Period Formula for Accelerating Elevator

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SUMMARY

The discussion centers on the period formula for a simple pendulum suspended in an accelerating elevator. The correct formula for the period T of the pendulum, considering the elevator's upward acceleration a, is T = 2π(L/(g + a))^(1/2). The participants clarify that this formula incorporates both gravitational acceleration g and the elevator's acceleration a, confirming its relevance in the context of non-inertial reference frames. The conversation emphasizes the importance of understanding the physical equivalence of gravitational fields and acceleration as articulated by Einstein in 1907.

PREREQUISITES
  • Understanding of simple harmonic motion and pendulum dynamics
  • Familiarity with gravitational acceleration (g) and its effects
  • Knowledge of non-inertial reference frames and their implications
  • Basic mathematical skills for manipulating equations
NEXT STEPS
  • Study the derivation of the period of a simple pendulum under varying conditions
  • Explore the implications of non-inertial frames in classical mechanics
  • Learn about the effects of acceleration on pendulum motion in different environments
  • Investigate Einstein's equivalence principle and its applications in physics
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the dynamics of pendulums in non-inertial reference frames.

hansel13
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Homework Statement


A simple Pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g, and a is:
2\pi*(L/a)^(1/2)
OR
2\pi*(L/(g+a))^(1/2)
OR
2\pi*(L/g)^(1/2)

Homework Equations


T = 2\pi*(L/g)^(1/2)

The Attempt at a Solution


Not sure where to start. It doesn't seem like there's really math involved here. I tried drawing a free body diagram, but that made things worse. I'm pretty sure it's the middle one, because the other 2 just don't make sense, because the formula needs to both a and g into account, right?
 
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Right.

"we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system." (Einstein 1907)
 
OK thanks
 

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