Ranking springs in terms of spring constant

[Avalanche]

Homework Statement

Homework Equations

Hooke's law. F = kΔx
ω = sqrt(k/m)

The Attempt at a Solution

For part A

F = mg = kΔx
k = mg/Δx

g is a constant so the spring constant is proportional to the mass and inversely proportional to the change in distance that the spring stretches

My answer is from smallest to largest spring constant: c < A = B < D

But the answer key says the answer is c < B = D < A

What am I doing wrong?

 

[haruspex]

My answer is from smallest to largest spring constant: c < A = B < D
But the answer key says the answer is c < B = D < A

That doesn't really constitute posting your attempt at a solution. You need to explain your reasoning.

 

[Avalanche]

That doesn't really constitute posting your attempt at a solution. You need to explain your reasoning.

Homework Statement

F = mg = kΔx
k = mg/Δx

g is a constant so the spring constant is proportional to the mass and inversely proportional to the change in distance that the spring stretches

Greater the mass, greater the spring constant. Longer the spring stretches, smaller the spring constant. Since C stretches by the largest amount and has a mass of only m, the spring constant is the smallest. A and B stretches by the same amount and have the same mass, the spring constants are equal. C has the largest spring constant because it stretches the spring by the same amount of A and B but has a larger mass.

 

[haruspex]

Greater the mass, greater the spring constant.

You seem to be equating the attached mass to the tension in the spring. That is not correct. The diagrams are not showing how the spring would be extended if subjected to the weight of the attached mass. For a start, the systems are horizontal, not vertical.
For this part of the question, ignore the masses. The diagrams are merely showing arrangements made by connecting up copies of some standard spring: two in parallel (A), two in series (C), or just one by itself (B, D).

 

[Avalanche]

Looking at the answer, I assume springs in parallel have greater spring constants, then springs by itself and springs in series have the smallest spring constant.

Is there a reason for this? Like an equation/relationship?

 

[haruspex]

Looking at the answer, I assume springs in parallel have greater spring constants, then springs by itself and springs in series have the smallest spring constant.

Is there a reason for this? Like an equation/relationship?

Suppose you have two identical springs with coefficient k. If one is stretched by x it is under tension kx. If I put two in parallel, what force will I need to pull with to get an extension of k (each)?
Then try the in series case.