Period of Oscillation of a Meter Stick

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SUMMARY

The discussion focuses on deriving the period of oscillation (T) for a meter stick suspended at one end, specifically evaluating the formula T = 2*sqrt(2I/mgL). Key variables include the rotational inertia (I), mass (m), gravitational acceleration (g), and length (L) of the meter stick. Participants emphasize the importance of understanding the small angle approximations for sine and cosine functions, as well as energy conservation principles in deriving the correct formula. The confusion surrounding the absence of π in the oscillation period formula is also addressed.

PREREQUISITES
  • Understanding of rotational inertia (I = mr²)
  • Familiarity with the concepts of gravitational acceleration (g)
  • Knowledge of simple harmonic motion and oscillation period formulas
  • Basic principles of energy conservation in mechanical systems
NEXT STEPS
  • Study the derivation of the period of oscillation for a physical pendulum
  • Learn about small angle approximations in trigonometry
  • Explore energy conservation methods in oscillatory systems
  • Investigate the role of rotational inertia in different physical systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for practical examples of period derivation in physical systems.

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Homework Statement



Measure the period of oscillation of a meter stick suspended at one end for small amplitudes.
Does T = 2*sqrt(2I/mgL) when I is the rotational inertia about one end? Derive this relation.


Homework Equations



I = rotational inertia
m = mass
g = gravitational acceleration
T = period of oscillation

I=mr^2

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

The Attempt at a Solution



I'm not going to lie, I have no idea where to start. Previous period of oscillation problems with a simple pendulum or a spring/glider system were based off of the formula for period that included 2pi divided by the angular frequency. I don't know where the pi went or what to do with the r value if I was to substitute it in. HELP!
 
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I think your equation is missing a π in it.


Anyhow, try considering that at a small angle, what the height is (above the lowest point).

For θ being small, what is cosθ and sinθ equal to?

Now try conserving some energy.
 

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