Consider a simple pendulum of length ℓ0 which oscillates with small amplitude at a place where g is uniform.
a. (a) Prove that if the length of the pendulum is multiplied by a factor k, its time period is multiplied by k.
b. (b) Using the result of part (a), show specifically that the length must be quadrupled to double the time period.
c. (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.