Period of a Pendulum The period T (in seconds) of a simple pendulum is a function of its l...

Period of a Pendulum The period T (in seconds) of a simple pendulum is a function of its length l (in feet) defined by the equation

where g ≈ 32.2 feet per second per second is the acceleration due to gravity.

(a) Use a graphing utility to graph the function T = T(l).

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(b) Now graph the functions T = T(l + 1), T = T(l + 2), and T = T(l + 3).

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(c) Discuss how adding to the length l changes the period T.

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(d) Now graph the functions T = T(2l), T = T(3l), and T = T(4l).

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(e) Discuss how multiplying the length l by factors of 2, 3, and 4 changes the period T.