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Determine the time period of a simple pendulum, if the mass of the rod is not negligible.Mass of the rod is M and mass of the bob is m.The length of the pendulum is L.

Determine the time period of a simple pendulum, if the mass of the rod is not negligible.Mass of the rod is M and mass of the bob is m.The length of the pendulum is L.

Grade:11

1 Answers

Rangan Sarkar
44 Points
6 years ago
Moment Of Inertia of rod about the fixed point is ML^2/3
Moment Of Inertia of bob about the fixed point is mL^2
now dispace the system by an angle A
so we know
Iα=torque
{(ML^2)/3 +mL^2}α = MgsinA*L/2 +mgsinA*L
as A is very small sinA=A
{(ML^2)/3 +mL^2}α =(Mg*L/2 +mg*L)A
so α is proportional to A so it is an SHM
which gives  ω^2=[(M+3m)L^2]/[3g(M+2m)]
now T=2π/w 
 

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