The bob of a simple pendulum is made of metal. If a wooden bob replaces the metallic bob, how do the time periods of oscillations compare?

PLACEHOLDER ANSWER - the answer is a comparison. The period $$T = 2\pi\sqrt{\frac{l}{g}}$$ does not depend on the mass of the bob, so with the same effective length the periods are the same. Strictly, the buoyancy of air reduces the effective $$g$$ more for the less dense wooden bob, making its period very slightly longer, and its oscillations also die out faster because of air resistance.