Why Should Spring Constants Be Added in a Dual-Spring System?

[quebecois22]

Hello,

Basically, we were asked to verify the dependence of the period of an object attached on both ends by a spring upon the mass of this object in Simple Harmonic Motion. Therefore, using different masses, we calculated the period each time and made a graph where the period is a function of the root of the mass, where (2*pi)/sqrt(k) should be the slope of the line, and we had to verify the value of k obtained from that slope, to the one measured before, where we would attach the springs in a vertical manner, and hang objects and measuring the spring constant for both springs.

Now, we measured both spring constants using the latter method to be 1.81 N/m, but using all our values and the slope, we get a k value of 4.01 N/m. Now our guess was that since we had two springs, the latter is probably the sum of both springs... but why?? Are we making the right assumption?

Why, in a two spring system, should one add both spring constants when doing calculations involving k??

Thank you.. :)

 

[Stonebridge]

Because if you stretch two springs, each with the same spring constant, the same amount, you get twice the force you would have got with only one spring.
As spring constant is force per unit amount of extension, then the combined value of k will be double the single value.