Calculating & Plotting Period of Vibration for Slender Rod AB

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SUMMARY

The discussion focuses on calculating and plotting the period of vibration for a slender rod AB attached to two identical collars in equilibrium. The analysis involves varying the angle β from 10 to 80 degrees and examining weight ratios of W/W_{AB} equal to 0, 2, and 4. The spring constant, denoted as k, is a crucial parameter in the calculations. The user seeks guidance on setting up the problem for accurate analysis and plotting.

PREREQUISITES
  • Understanding of basic mechanics and equilibrium principles
  • Familiarity with the concept of the spring constant (k)
  • Knowledge of vibration analysis and period calculations
  • Ability to plot mathematical functions using graphing tools
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  • Research the mathematical derivation of the period of vibration for oscillating systems
  • Learn how to apply the principles of equilibrium to dynamic systems
  • Explore graphing software options for plotting functions, such as MATLAB or Python's Matplotlib
  • Investigate the effects of varying weight ratios on the dynamics of slender rods
USEFUL FOR

Students studying mechanics, engineers involved in dynamic system analysis, and anyone interested in understanding the behavior of oscillating systems in equilibrium.

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Homework Statement



The slender rod AB of weight W_{AB} is attached to two identical collars, each of weight W. The system lies in a horizontal plane and is in equilibrium in the position shown when the collar A is given a small displacement and released. Calculate and plot the period of vibration for values of the angle β from 10 to 80 degrees for weight ratios \frac{W}{W_{AB}} of 0, 2, and 4.

http://image.cramster.com/answer-board/image/20095101932446337758076418525009540.jpg

I'm looking for help as to how to set the problem up that's all! Any help is appreciated!

Homework Equations





The Attempt at a Solution

 
Last edited by a moderator:
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What does the k in the diagram represent?
 
spring constant, i would guess.
 
Yes it's the spring constant
 

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