The period of torsional oscillations can be described by the formula:
T1=aqF(z) (1)
where z signifies the distance from the rod center to the centers of the nuts, and F(z) stands for a function that depends on z only.
It can be shown that the function F(z) in formula (1) has the following form:
F(z)=A+Bz2 (2)
where A,B refer to some constant values independent of the parameters a and z.
3.1 Measure the dependence of the period of torsional oscillations T1 on the distance between the threads a, plot a graph of the resulting dependence. Take measurements when the nuts are at the rod ends with z=17 cm.
3.2 Based on experimental data, prove the validity of formula (1) and determine the exponent q. An error estimate is not required here.
3.3 Fix the suspension threads at a distance of a=10 cm. Measure the period of torsional oscillations as a function of the position of the nuts z. Plot a graph of the resulting relationship. It is unnecessary to take measurements when the nuts are closer to the center of the rod than the threads.
3.4 Prove the applicability of formula (2) to describe your experimental data.
3.5 Calculate the values of the coefficients A,B and estimate their errors. Please note that values a,z must be measured in centimeters.