Which Spring Has a Larger Displacement?

[smhippe]

Homework Statement

An 8 kg mass is hanging from two springs that are attached to the ceiling as shown in the figure. The spring constant of spring A is 165 N/m and the spring constant of spring B is 123 N/m. Which spring has a larger displacement?
Note: Spring A is attached to the ceiling on the left. It is angled at positive 60 degrees from the negative x-axis or (4$$\pi$$)/6. Spring B is on the right side angled at positive 45 degrees from the positive x-axis or ($$\pi$$)/2. Both are attached to their respective corners of the mass (particle).

Possible Answers:
Spring A
Spring B
Springs have equal displacement
It's impossible to calculate displacement without knowing the equilibrium length.

Homework Equations

Energy conservation and simple kinematics. ($$\Delta$$)U$$_{}g$$
($$\Delta$$)U$$_{}s$$
($$\Delta$$)K

The Attempt at a Solution

This problem is stumping me...
But, what I tried doing is setting the change in potential energy for gravity plus the change in potential energy for the spring equal to zero. I figure we can do this because there are no friction forces or drag in this case. Then we set the change in height equal to the change in displacement (using sin in the respective cases). But since the question has two springs I am a little confused on how to handle that. But the bigger question is, do we have to know the equilibrium length to solve it?

 

[rock.freak667]

The spring constant is the force needed to produce unit extension.

So the higher the spring constant, the more force needed to cause unit extension.

Knowing this now, which would would extend more?

 

[smhippe]

Spring B. That's what my gut feeling was.
So if I understand everything correctly we don't need to know equilibrium length. If we were to actually solve this problem would we need it then?

 

[rock.freak667]

Spring B. That's what my gut feeling was.
So if I understand everything correctly we don't need to know equilibrium length. If we were to actually solve this problem would we need it then?

I don't think you will need it even if it is placed at that angle like that.