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=0.39 kg) and the other of metal (mass=0.72 kg) They are set into oscillation and execute simple harmonic motion. Determine the period of (a) the wood pendulum and (b) the metal pendulum

Answer 1

From definition

dt2

and Torque $\tau =-I\alpha$

$Mg\theta =-Ix\frac{\mathrm{d^{2}}\theta }{\mathrm{d} t^{2}}$

The moment of inertial of the rod about one end is $I=\frac{ML^{2}}{3}$

The time period of the rod about one end is $T=2\pi \sqrt{\frac{I}{MgR}}$

  $T=2\pi \sqrt{\frac{\frac{ML^{2}}{3}}{MgL/2}}$

3g

And since the length is same for both the lens, the time period also same, the time period is independent on mass of the rods.