A pendulum is constructed from two identical uniform thin rods a and b each of length L and mass m, connected at right angles to form a ‘T by joining the centre of rod a to one end of rod b. The ‘T’ is then suspended from the free end of rod b and the pendulum swings in the plane of the ‘T’.
(a) Calculate the moment of inertia I of the ‘T’ about the axis of rotation.
(b) Give expressions for the kinetic and potential energies in terms of the angle θ of inclination to the vertical of the pendulum.
(c) Derive the equation of motion of the pendulum.
(d) Show that the period of small oscillations is
2π√17L/18g