A student investigates how the time period of a simple pendulum depends on its length.
(a) Define the term "time period" of a simple pendulum.
(b) Justify, with algebraic reasoning, the statement: "If the length of a simple pendulum is increased nine times, its time period becomes three times the original value."
(c) Using similar reasoning, predict how the frequency of a simple pendulum will change if its length is reduced to one–quarter of its original value. Give your answer as a numerical factor.