Simple pendulum and harmonic motion

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SUMMARY

The period of a simple pendulum with a length of 5.20 m, when subjected to an upward acceleration of 5.90 m/s², requires adjustment to the standard formula due to the non-inertial frame of reference. The correct formula for the period T in this scenario is T=2π*(sqrt(L/g')), where g' is the effective gravitational acceleration, calculated as g' = g + a (where g = 9.8 m/s² and a = 5.90 m/s²). Thus, the effective gravitational acceleration becomes 15.70 m/s², leading to a period of approximately 2.54 seconds.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with the formula for the period of a pendulum
  • Knowledge of gravitational acceleration and its effects
  • Concept of non-inertial reference frames
NEXT STEPS
  • Study the derivation of the pendulum period formula under varying gravitational conditions
  • Explore the effects of acceleration on oscillatory motion
  • Learn about non-inertial reference frames in classical mechanics
  • Investigate the implications of effective gravitational acceleration in different scenarios
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to explain the effects of acceleration on pendulum behavior.

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Homework Statement



A simple pendulum is 5.20 m long. What is the period of simple harmonic motion for this pendulum if it is hanging in an elevator that is accelerating upward at 5.90 m/s2?


Homework Equations



T=2pi*(sqrt(L/g))

The Attempt at a Solution



all I did was plug in the value of the length of the pendulum into the equation like so:
T=2pi*(sqrt(5.2/9.8))=4.58s
but this answer is not right? I'm so confused as to what I am supposed to do and why I am given acceleration if I don't even need it.
 
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If you know how to derive this equation you are using, I would go through it and look at where the gravitational acceleration, g, comes in. If the pendulum is feeling a vertical acceleration from the elevator now, in addition to the gravitational acceleration, how would that affect your derivation/equation?
 
You're not in a stationary frame of reference. You're in an accelerating frame of reference. Think about it. When you are in an elevator that is accelerating upward (e.g. when it first begins to move) do you feel lighter, heavier, or nothing at all?

It's almost as if a mysterious force has cropped up ;)
 

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