Question

A physical pendulum consists of a disc of radius R and mass m fixed at the end of a rod of mass m and length l .


(a) Find the period of the pendulum for small angles of oscillation. Express your answer in terms of m, R, l and acceleration due to gravity g as needed (enter m for m, R for R, l for l, g for g and pi for π).

Tfixed=


(b) For small angles of oscillation, what is the new period of oscillation if the disk is mounted to the rod by a frictionless bearing so that it is perfectly free to spin? Express your answer in terms of m, R, l and acceleration due to gravity g as needed (enter m for m, R for R, l for l, g for g and pi for π).

Tfree=

Answer 1

Tfixed=2*pi*((8*l^2+3*R^2)/(9*g*l))^(1/2)

but i haven't yet checked my answer for Tfree.

Answer 2

Tfree=2*pi*((8*l^2)/(9*g*l))^(1/2)