Question

1. A physical pendulum has a bob with massMand an arm with length`and massm.(a) Using the small angle approximation, find the period of the pendulum,Tp.(b) A simple pendulum has periodT0= 2π√`g. What is the fractional difference betweenTpandT0?

A physical pendulum has a bob with mass M and an arm with length ( and mass m (a) Using the small angle approximation, find the period of the pendulum, Tp (b) A simple pendulum has period To 2πν, what is the fractional difference between Tp and To?

Answer 1

A physical pendulum has a bob with mass M and an arm with length and mass m. c = -mg dem sin theta For small angle sin theta almostequalto theta I 'theta' + mg dem theta = 0 theta + (mg dem/I) theta = 0 theta + w^2 theta = 0 T = 2 pi/w = 2 pi squareroot I/mg den I = (ml^2) + (ml^2/3) = (m + m/3) l^2 dcm = m (l/2) + ml/(m + m) + l/2 ((m + 2m)/(m + m)) T = 2 pi squareroot (n + n/3) l^2/l/2 (m + 2m)/(m + m) (m + m) g