Chapter 2.5, Problem 86AYU

88. 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 $T\text{ = 2}\pi \sqrt{\frac{l}{g}}$

where $g\approx \text{ 32}\text{.2}$ feet per second per second is the acceleration due to gravity.

(a) Use a graphing utility to graph the function $T\text{ = }T\left(l\right)$.

(b) Now graph the functions $T\text{ = }T\left(l\text{ + 1}\right)$, $T\text{ = }T\left(l\text{ + 2}\right)$, and $T\text{ = }T\left(l\text{ + 3}\right)$.

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

(d) Now graph the functions $T\text{ = }T\left(2l\right)$, $T\text{ = }T\left(3l\right)$, and $T\text{ = }T\left(4l\right)$.

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