Hello,

I am having a problem with trying to figure out how my book came up
with the solution to an odd number problem, it is stated as follows,
"A student hangs masses on a spring and measures the spring's
extension as a function of the applied force in order to find the
spring constant k. Her measurements are:

(mass (kg), Extension(cm)) = ( 200 , 5.1 ) , ( 300 , 5.5 ) , ( 400 ,
5.9 ) , ( 500 , 6.8 ) , ( 600 , 7.4 ) , ( 700 , 7.5) , ( 800 , 8.6 ) ,
( 900 , 9.4 )

There is an uncertainty of .2 in each measurement of the extension. The
uncertainty in the mass is negligible. For a perfect spring, the
extension DeltaL of the spring will be related to the applied force by
the relation k(DeltaL)=mg, where DeltaL=L-L0 and L0 is the unstretched
length of the spring. Use these data and the method of least squares to
find the spring constant k, the unstretched length of the spring L0,
and their uncertainties. Find Chi-Squrare for the fit and the
associated probability."

I first approached this problem by setting up the equation k(DeltaL)=mg
so it can be used to solve for L0 and K via the least square method,
since it sounds like that is how the problem wants us to solve for L0
and K. The result was L=g/k*m+L0.

However, I quickly ran into a problem
since the measurements the problem gives you are the extensions and not
the total length; thus, you cannot use my equation to solve for L0 and
k via the least square method with the measured values given. I next
consider the possibility that they just wanted you to solve for k via
the least square method and then use the resulting value given to solve
for L0. I switched the equation around and came up with
(DeltaL)=g/k*m. I applied the least square method to solve for g/k and
came up with a value and its uncertainty. I next tired setting up a
system of linear equations to solve for L0, but I quickly found myself
going in circles since there really is no way to setup a system of
equations to solve for L0 (or at least that I saw). What am I over
looking?