Oscillation vs. Pendulum Periods

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SUMMARY

The discussion centers on determining the period of oscillation for a uniform thin rod compared to a simple pendulum. The rotational inertia of the rod is given as ML²/3, where M is the mass and L is the length. The user aims to equate the oscillation period T of the rod, expressed as T = sqrt(I/k), with the pendulum period T = 2π(sqrt(L/g)). The challenge lies in finding the torsion constant k, which is essential for solving the equations.

PREREQUISITES
  • Understanding of rotational inertia and its calculation.
  • Familiarity with the physics of oscillations and pendulums.
  • Knowledge of the relationship between torque and angular motion.
  • Basic grasp of the concepts of torsion constants in oscillatory systems.
NEXT STEPS
  • Research how to calculate the torsion constant k for different materials and shapes.
  • Explore the derivation of the period of oscillation for various physical systems.
  • Study the relationship between rotational dynamics and linear motion in oscillatory systems.
  • Investigate experimental methods to measure the period of oscillation for a thin rod.
USEFUL FOR

Physics students, educators, and anyone studying dynamics and oscillatory motion in mechanical systems.

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Homework Statement



The rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of length:

Homework Equations





The Attempt at a Solution



My original plan was to use a system of equations with:

T = sqrt(I/k) (oscillation, where k is torsion constant)
and
T = 2pi(sqrt(L/g)) (simple pendulum.)

However, I don't know the torsion constant and have no means to find it. What's my first step?
 
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Should I get k in other terms and substitute?
 

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