A student investigates how the time period of a simple pendulum depends on its length.
a. (a) Define the term "time period" of a simple pendulum.
b. (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. (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.