Consider a simple pendulum of length ℓ0 which oscillates with small amplitude at a place where g is uniform.
(a) Prove that if the length of the pendulum is multiplied by a factor k, its time period is multiplied by k.
(b) Using the result of part (a), show specifically that the length must be quadrupled to double the time period.
(c) A laboratory pendulum has an initial length of 1.20m. By what percentage should the length be altered so that its frequency increases by 2%? State clearly whether the length should be increased or decreased, and calculate the new length to the nearest millimetre.