MHB Dynamics Coursework; Angular Velocity, Springs, Force

[DTskkaii]

Question:
The flat circular disc rotates about a vertical axis through O with a constant angular velocity of 240rpm. Prior to rotation, each of the 0.5kg sliding blocks has the position x=25mm with no force in its attached spring. Each spring has a stiffness of 400N/m, Neglect any friction between the blocks and the slots, and neglect the mass of the springs.

(a) Determine the value of x for each spring
(b) Calculate the normal force N exerted by the side of the slot on the block

I have attached the diagram.

Relevant equations
Not yet completely sure. If someone knows of a resource towards rotational velocity, that would be helpful, but I will update this section as soon as I have identified appropriate equations.
The attempt at a solution
As per above, I will upload something as soon as I can get a solid attempt down. I'm honestly incredibly lost on this question, it just seems like there are so many aspects happening at once.

 

[CaptainBlack]

Question:
The flat circular disc rotates about a vertical axis through O with a constant angular velocity of 240rpm. Prior to rotation, each of the 0.5kg sliding blocks has the position x=25mm with no force in its attached spring. Each spring has a stiffness of 400N/m, Neglect any friction between the blocks and the slots, and neglect the mass of the springs.

(a) Determine the value of x for each spring
(b) Calculate the normal force N exerted by the side of the slot on the block

I have attached the diagram.

Relevant equations
Not yet completely sure. If someone knows of a resource towards rotational velocity, that would be helpful, but I will update this section as soon as I have identified appropriate equations.
The attempt at a solution
As per above, I will upload something as soon as I can get a solid attempt down. I'm honestly incredibly lost on this question, it just seems like there are so many aspects happening at once.

In the rotating reference frame you have the following forces acting on the left hand block (the motion of the other is the same after the appropriate transformation):

A radially outward (ficticious) force \(m r \omega^2 \).

The normal reaction force from the side of the slot \(N\) in the +ve horizontal direction.

The spring force \(k(x-25)\) in the -ve vertical direction.

Since the block is constrained to move in the vertical by the slot the normal reaction will always balance the horizontal component of the radial force.

CB