Rational motion combined with 2 springs

[Maggie]

Homework Statement

Block A (0.40 kg) and block B (0.6 kg) are on a frictionless table (see figure). Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B. When the blocks are in uniform circular motion about 0, the springs have lengths of 0.60 m and 0.40 m, as shown. The springs are ideal and massless, and the linear speed of block B is 2.0 m/s. If the distance that spring 2 stretches is 0.055 m, the spring constant of spring 2 is closest to (in N/m)

Relevant Equations

F=kx
Fc=mv^2/R
ω=v/r

I first calculated the speed of two blocks using angular speed, then find the centripetal force of them, but I don't know how to proceed my calculation, what value should I plug into Hooke's law?

 

[Lnewqban]

Welcome, Maggie!

Can you show us your work so far?

The centripetal acceleration makes both springs stretch up to each of the given lengths.
Spring 2 was originally 0.055 m shorter.
It seems that the problem is asking for the constant of spring 2 only.

 

[haruspex]

You know how much spring 2 has been stretched. In order to find its constant, what do you need to work out?

 

[Maggie]

Welcome, Maggie!

Can you show us your work so far?

The centripetal acceleration makes both springs stretch up to each of the given lengths.
Spring 2 was originally 0.055 m shorter.
It seems that the problem is asking for the constant of spring 2 only.

I find the angular velocity is 2rad/s, and speed of A is 1.2m/s, the Fc of B is 2.4N, I suppose that k=2.4/0.055=43.6?

 

[Maggie]

You know how much spring 2 has been stretched. In order to find its constant, what do you need to work out?

I think the force, is that centripetal force of Block B only?

 

[haruspex]

I think the force, is that centripetal force of Block B only?

Yes, and yes.

 

[Maggie]

Yes, and yes.

Thank you so much now I got that!