Solve the Pendulum Beam Problem with Simple Equations | Homework Help

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The discussion focuses on solving the pendulum beam problem, where a uniform steel beam swings with a period of 1.10 seconds. The initial attempt to calculate the length using the simple pendulum formula is incorrect because it assumes a point mass at the end, while the beam's mass is distributed along its length. To solve the problem accurately, one must derive the correct formula for a physical pendulum, taking into account the moment of inertia and the center of mass. The gravitational force acts at the center of mass, which complicates the calculation. Understanding these principles is essential for finding the correct length of the beam.
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Homework Statement



On the construction site for a new skyscraper, a uniform beam of steel is suspended from one end. If the beam swings back and forth with a period of 1.10 s, what is its length?

Homework Equations



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

The Attempt at a Solution



(1.1/(2*3.14))^2*9.81=L

L=.3007m

This is wrong however and I don't understand why.
 
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PhyzicsOfHockey said:

Homework Statement



On the construction site for a new skyscraper, a uniform beam of steel is suspended from one end. If the beam swings back and forth with a period of 1.10 s, what is its length?

Homework Equations



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

The Attempt at a Solution



(1.1/(2*3.14))^2*9.81=L

L=.3007m

This is wrong however and I don't understand why.
The period equation you have written is for a simple pendulum with a point mass at the end. You cannot use it for this case, since the mass is uniformly distributed along the beam. You must find or derive the correct formula for this case.
 
This is the case of physical pendulum. The gravitational force acts at centre of mass and u can assume a point mass hanging there and then calculate.
 
no, you will need the moment of inertia of the steel rod as well
 

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