The frequency of two parallel springs and one weight system

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SUMMARY

The discussion centers on calculating the angular frequency of a system involving two parallel springs and a weight. Key equations referenced include Hooke's Law (F = -kx) and the potential energy formula (U = 1/2*k*x^2). Participants emphasize the importance of considering the moment of inertia (MoI) and angular acceleration in the analysis. The consensus is that the sum of moments must account for the MoI of the system, which is not zero, thus affecting the overall dynamics.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Familiarity with the concept of moment of inertia (MoI)
  • Knowledge of angular acceleration and its implications in rotational dynamics
  • Basic grasp of potential energy in mechanical systems
NEXT STEPS
  • Study the derivation of angular frequency in systems with springs and weights
  • Learn about the calculation of moment of inertia for composite systems
  • Explore the relationship between angular acceleration and torque in rotational dynamics
  • Investigate examples of oscillatory motion in mechanical systems
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Students in physics or engineering, particularly those studying mechanics, as well as educators seeking to clarify concepts related to angular frequency and rotational dynamics.

ltnghia1304
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Homework Statement


I want to find the angular frequency of the system below
18426564_1972065893013072_43662875_o.jpg

Homework Equations


F = -kx
U = 1/2*k*x^2

The Attempt at a Solution


18426570_1972072309679097_1115670989_o.jpg

18472001_1972072313012430_1129210577_o.jpg


But here's the answer:
18426731_1972065903013071_83517209_o.jpg


18426790_1972065909679737_1688739849_o.jpg


I don't know how come this solution. Any one help me? Thank you so much.
 

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I do not understand even your first equation. It looks like a sum of moments about left hand end equals zero. But there will be an angular acceleration here, and the system has a moment of inertia about that axis.
About what point does it not have any MoI?
 
haruspex said:
I do not understand even your first equation. It looks like a sum of moments about left hand end equals zero. But there will be an angular acceleration here, and the system has a moment of inertia about that axis.
About what point does it not have any MoI?

Yes I used the sum of moments. Actually I also haven't get the point of this problem. Just think that it will be balance like that
 
ltnghia1304 said:
I used the sum of moments
OK, but the standard equation, relative to a specified axis, is Σmoment=MoI * angular acceleration. The bar will in general have an angular acceleration, and the MoI of the bar+mass about the ends of the bar is not zero. So the sum of the moments will not be zero.
As I asked before, about what axis does the bar+mass have zero MoI?
 

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