What is the Extension Produced in Springs Arranged in Series and Parallel?

[timeheist]

Homework Statement

I'm not so sure about the following:

You have 3 set-ups, using identical springs of the same length and stiffness. In the first you have a single spring with mass m attached to it, producing extension x. In the second you have identical springs in series, attached end to end and then with mass m attached to the bottom. In the third you have two identical springs in parallel, sharing mass m load.

What would be the extension produced in each set-up?

Homework Equations

f= -kx

The Attempt at a Solution

In the third case with the springs in parallel, since the whole thing is in equilibrium and assuming the length of the strings attaching the springs to the mass are the same, would the weight acting on them be halved, so the extension produced on each spring be x/2?

With the springs in series, I'm really not sure what to think. Not sure whether to treat the springs as one franken-spring, or think of spring 1 and spring 2.

Thanks for any help

 

[td21]

I suggest you try google: "equivalent spring constant" as a starting point. This may be helpful. Your equation is correct and the answer should depend on the value of k.