Sliding sleeve on a rotating bar with two springs

In summary, the problem involves a sleeve of mass m fixed between two identical springs with stiffness k, able to slide without friction over a horizontal bar. When the arrangement rotates at a constant angular velocity w, the period of small oscillations of the sleeve can be found using the equation T=2âˆ/(k/m-ω2)1/2. There is no simple solution without using polar coordinates.
  • #1
andyrk
658
5

Homework Statement


P45) In the arrangement shown in figure, the sleeve M of mass m is fixed between two identical springs whose combined stiffness is equal to k. The sleeve can slide without friction over a horizontal bar AB. The arrangement rotates with a constant angular velocity w about a vertical axis passing through the middle of the bar. Find the period of small oscillations of the sleeve. At what values of w will there be no oscillations of the sleeve?



2. Homework Equations
T=2âˆ/(k/m-ω2)1/2


The Attempt at a Solution


I got this answer by following the pseudo force approach but got stuck when I tried to do it with the normal method without pseudo force. Can we do it without using pseudo forces? And if yes then how?
 

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  • #2
Is anyone there to reply?
 
  • #3
Are you familiar with how to express acceleration in polar coordinates?
 
  • #4
No. Its not in the curriculum I am doing.
 
  • #5

FAQ: Sliding sleeve on a rotating bar with two springs

How does the sliding sleeve on a rotating bar with two springs work?

The sliding sleeve on a rotating bar with two springs works by using the springs to create a force that pushes the sleeve along the bar as it rotates. The springs are connected to the sleeve and the bar, creating a tension force that causes the sleeve to move.

What is the purpose of the two springs in this mechanism?

The two springs in this mechanism serve to create a balanced force that allows the sleeve to move smoothly along the rotating bar. They also help to distribute the force evenly, preventing any one spring from becoming overloaded.

How does the rotation of the bar affect the movement of the sliding sleeve?

The rotation of the bar is what drives the movement of the sliding sleeve. As the bar rotates, it creates a force that is transferred to the sleeve through the springs, causing it to move along the bar.

Can the sliding sleeve on a rotating bar with two springs be used for any other applications?

Yes, this mechanism can be used in a variety of applications, such as in mechanical devices or as part of a larger system. It can also be adapted for different purposes by adjusting the size and strength of the springs and the rotating bar.

Are there any drawbacks to using a sliding sleeve on a rotating bar with two springs?

One potential drawback is that the springs may wear out over time and need to be replaced. Additionally, if the rotating bar is not properly lubricated, it may cause friction and affect the smooth movement of the sliding sleeve. Regular maintenance and care can help to prevent these issues.

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