Question

Find the periods of two physical pendulums consisting of identical thin rigid rods of length L = 138 cm. The first rod is pivoted about it's upper end, while the second rod is pivoted at a small hole drilled through the rod at a distance d = 103 cm from it's lower end, see the picture below. Note that the mass of the rod is not important — it cancels out. If it helps, take m = 1 kg.

g Ί p - - - - - m - m (1) (2)

The period of the first pendulum, T₁ =  Unit in s

The period of the second pendulum, T₂ =  Unit in s

Answer 1

taking Pivot as reference Potential energy V rog Lolo Position of stable OV 0 energy equilibrium: =) IngLfindzo => [ 030 Tore constant, ka - du do2 100= ngllors (o=o= mg so, Time period, T=an IT PT ne ingh va (D): time period, 7= 271 J SRT 138x10? 9.8 50.62PX 14.08 Ta Rixo.1 x 138 9.8 T= 0.628 X 3,752 12.356 S (2) Similarly, time period, T = 20 And ) व T= 2T X 103 X 10-2 9.8 2 TTXD. IX 103 9.8 t = 0.628 x Viosi = 0.628 X 3.242 += 2.0368 Ang