Calculating & Plotting Period of Vibration for Slender Rod AB

In summary, the problem involves a system with a slender rod attached to two collars in equilibrium. The system is then displaced and the period of vibration is calculated for varying weight ratios and angles. The diagram represents the spring constant.
  • #1
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Homework Statement



The slender rod AB of weight [tex]W_{AB}[/tex] is attached to two identical collars, each of weight [tex]W[/tex]. 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 [tex]\frac{W}{W_{AB}}[/tex] 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

 
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  • #2
What does the k in the diagram represent?
 
  • #3
spring constant, i would guess.
 
  • #4
Yes it's the spring constant
 

Related to Calculating & Plotting Period of Vibration for Slender Rod AB

What is the equation for calculating the period of vibration for a slender rod AB?

The equation for calculating the period of vibration for a slender rod AB is T = 2π√(L/g), where T is the period in seconds, L is the length of the rod in meters, and g is the acceleration due to gravity in m/s^2.

What is the significance of calculating the period of vibration for a slender rod AB?

Calculating the period of vibration for a slender rod AB allows us to determine the time it takes for the rod to complete one full cycle of vibration. This information is important in understanding the behavior and stability of the rod under different conditions.

How do you plot the period of vibration for a slender rod AB?

To plot the period of vibration for a slender rod AB, you will need to first calculate the period for different lengths of the rod, using the equation T = 2π√(L/g). Then, you can plot a graph with the length of the rod on the x-axis and the period on the y-axis.

What factors affect the period of vibration for a slender rod AB?

The period of vibration for a slender rod AB is affected by the length of the rod and the acceleration due to gravity. Other factors that may affect the period include the material and density of the rod, as well as any external forces acting on the rod.

Can the period of vibration for a slender rod AB be changed?

Yes, the period of vibration for a slender rod AB can be changed by altering the length of the rod or the acceleration due to gravity. It can also be affected by changing the material or density of the rod, or by applying external forces to the rod.

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