Question

Two physical pendulums (not simple pendulums) are made from meter sticks that are suspended from the ceiling at one end. The sticks are uniform and are identical in all respects, except that one is made of wood (mass = 0.16 kg) and the other of metal (mass = 0.88 kg). They are set into oscillation and execute simple harmonic motion. Determine the period of (a) the wood pendulum and (b) the metal pendulum.
(a) T = ? s
(b) T = ? s

Answer 1

time period   physical pendulum

T = 2π√ I/ mgh

or T = 2π√ 2L/3g

   from the above equations time period does not depend on mass

time period T = 1.63s

   so both pendulum have same time period.

Answer 2

so the moment of inertial of a stick about the end is 1/3ML²

The period of physical pendulum is T=2π√I/mg(L/2), plugging in I gives us T=2π√2L/3g=1.64 s. Notice that the m canceled so both will have the same period.

Answer 3