Oscillation vs. Pendulum Periods

In summary, the rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is the length. When hung vertically and set into small amplitude oscillation, a rod with L=1.0 m will have the same period as a simple pendulum of length L=sqrt(3/2) m. The first step to solve for the torsion constant (k) is to substitute the given values into the equations T=sqrt(I/k) and T=2pi(sqrt(L/g)).
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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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  • #2
Should I get k in other terms and substitute?
 

Related to Oscillation vs. Pendulum Periods

1. What is the difference between oscillation and pendulum periods?

Oscillation refers to the repetitive back and forth movement of an object about its equilibrium position. Pendulum period, on the other hand, refers to the time it takes for a pendulum to complete one full swing.

2. How are oscillation and pendulum periods related?

Oscillation and pendulum periods are related through the length of the pendulum. The longer the pendulum, the longer the period of oscillation and pendulum. This relationship is known as the "pendulum law" or "pendulum equation."

3. Can an object have both oscillation and pendulum periods?

Yes, an object can have both oscillation and pendulum periods. Any object that has a back and forth motion can be considered to have an oscillation period, while a pendulum period can be observed in objects with a specific length and mass attached to a fixed point.

4. How does the mass and length of a pendulum affect its period?

The mass and length of a pendulum have a direct effect on its period. A heavier mass will have a longer period, while a longer length will result in a longer period. However, the effect of mass is not as significant as the effect of length on the period of a pendulum.

5. Can the period of a pendulum be calculated?

Yes, the period of a pendulum can be calculated using the pendulum equation: T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This equation assumes that the pendulum is in a vacuum with no air resistance.

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