The magnitude of this restoring force is directly proportional to the stretch in the relation below.
From the relation it is evident that if a plot of F as a function of ∆ l has a linear proportion. This provides confirmation that the spring conforms to Hookes Law and enables us to find k mathematically. (Sears, 1981)
The objective of this experiment is to study the behavior of ordinary springs in static and dynamic situations. We will determine the spring constant, k , (K which is the stiffness of the spring), for an individual spring using both Hookes Law and the properties of an oscillating spring system.
Figure 2 indicates that for forces greater than about 4.5N (notice intercept of best fit), there is a linear relation between force and extension. For small loads such a relationship fails, since the fit curve does not intercept the y axis at zero. It is assumed that this is caused by an initial "set" in the spring which requires some initial load to overcome. This is apparent if one stretches the spring manually and then releases it. It seems to snap shut at the last moment.
These were used to plot the line on the graph. The slope of the line, ignoring loads of less than 4.5N, was found to be 147.36 N/m. From Equation 1, we see that we need to multiply this quantity by g to calculate a value for the spring constant of k = 217.4 ± 1.8 N/m.
A graph of force versus the magnitude of displacement resulted in the expected straight line in the range of forces examined and is consistent with Hooke’s law. The slope of this line, 147.36 N/m, is the spring constant, which agrees with value found by taking the average of the calculated spring constant. The intercept for the best fit straight line intersects close to the origin, which is also consistent with Hooke’s law.
The potential sources of error in this experiment are due to the precision of the location measurement using the meter rule and the accuracy of the slotted masses used. The meter