Is the slope of a Weight (force, in N) vs. Length (meters, m) graph- in reference to springs adhering to Laws of SHM- the value of k (Spring Constant, of units N/m) for that point's represented situation?

Question

amonoconnor · Answer

Also, so if I plot a scatter plot of values (weight, length), and average the individual quotients of each point (weight/length), will the slope of this scatterplot's best-fit line be the entire situation's mean K?

amonoconnor · Answer

:) thanks again !

amonoconnor · Answer

Is my question coherent? Do I need to re-phrase anything?

anonymous · Answer

Consider the slope formula: $$m=\Delta y/\Delta x$$Now put the formula in terms of the units of your graph:$$m=\Delta F/\Delta x$$Now if you rearrange Hooke's Law you get:$$k=-F/x$$So, yes, the slope of your Force vs distance graph is the spring constant.  Note that in Hooke's Law the negative sign just indicates that the force works in the direction opposite the spring's deformation. 

The slope of the best fit line will give you the best fit spring constant. Specifically using your method you will get the average spring constant.

amonoconnor · Answer

Okay... Sweet. Also, I just sort of had the epiphany that I must subtract the given length of the spring with no weight from every other length, in order to have the values of x, displacement, before I can use the Hook's Law formula, right?

agent0smith · Answer

^yes, x is measured from the zero point.

amonoconnor · Answer

Alrighty. I believe I known what I need to do now :) lols, sleep shall wait for me. Thank you for taking a look at this, and sleep well!