Question

have performed an experiment of simple harmonic motion and the values I got
Mass(g) Distance (m)
200 0.438
250 0.398
300 0.345
350 0.312
400 0.297
450 0.281
500 0.259

I would like to know how to calculate the spring constant... since I have been having weird values, if someone could please give me each value for k I will deeply appreciate it....

Answer 1

The spring constant is the change in spring length divided by the change in force.

If your spring obeyed Hooke's law, the distance would change by the same amount each time a 50g mass was added. That does not seem to be what is happening. Your curve is not linear. Either there is something wrong with the spring, or with the measurements

In your case, a 300 g (0.30 kg) added mass, which weighs 2.943 N, changes the spring length by 0.438-0.259 = 0.179 m

An average value for the spring contant is therefore
k = 2.943/0.179 = 16.44 N/m

Answer 2

I forgot to mention that the experiment is to teach us error analysis methods...


I have to get the values of k for each interval

Mass(g) Distance (m)
200 0.438
250 0.398
300 0.345
350 0.312
400 0.297
450 0.281
500 0.259

the values for k I got were
k (N/m)
0
61.3
55.5
104
261
276
223
respectively

because I substracted the values of each distance with the previous one... do I have to substract all the distances from the first one in order to get the correct calculations???