# Homework Help: Sliding sleeve on a rotating bar with two springs

1. Dec 22, 2013

### andyrk

1. The problem statement, all variables and given/known data
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. Relevant equations
T=2âˆ/(k/m-Ï‰2)1/2

3. 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?

#### Attached Files:

• ###### image010.gif
File size:
6.9 KB
Views:
174
2. Dec 22, 2013

### andyrk

3. Dec 22, 2013

### TSny

Are you familiar with how to express acceleration in polar coordinates?

4. Dec 22, 2013

### andyrk

No. Its not in the curriculum I am doing.

5. Dec 22, 2013

### TSny

I'm afraid I don't see a nice way to do it other than using polar coordinates .