We are given that a pendulum has the following half periods for different masses.
For the 30 cm pendulum we have:
[tex]\frac{T_1}{2}\approx1.0s[/tex]Therefore, the period is determined by multiplying the half period by 2:
[tex]T_1\approx2s[/tex]For the 50 cm pendulum we have that half the period is:
[tex]\frac{T_2}{2}\approx1.3s[/tex]Therefore, the period is:
[tex]T_2=2.6s[/tex]For the 70 cm pendulum we have that half the period is:
[tex]\frac{T_3}{2}=1.6s[/tex]The period is:
[tex]T_3=3.2s[/tex]Question 1: Did the period of the pendulum swing depend on the mass of the bob?
We notice that for different masses the period is approximately the same, therefore, the period of the pendulum is independent of the mass.
Question 2: On the length of the string?
The period varies with the length therefore the period is dependent on the length of the pendulum,
Question 3: How does your data relate to the pendulum equation?
The pendulum equation is the following:
[tex]T=2\pi\sqrt{\frac{L}{g}}[/tex]Where "L" is the length and "g" is the acceleration of gravity.
For the length of "L = 30 cm" we have:
[tex]T=2\pi\sqrt{\frac{0.3m}{9.8\frac{m}{s^2}}}\approx1s[/tex]For the "L = 50cm" we have:
[tex]T=2\pi\sqrt{\frac{0.5}{9.8}}\approx1.4s[/tex]For the 70 cm length we have:
[tex]T=2\pi\sqrt{\frac{0.7}{9.8}}=1.6s[/tex]Therefore, the measurements are consistent with the results of the pendulum equation.