The period T (in seconds) of a simple pendulum is a function of its length l (in feet), given by T(l) = 2pi sq root of l/g, where g = 32.2 feet per second per seconds is the acceleration of gravity. Express the length l as a function of the period T.

Question

The period T (in seconds) of a simple pendulum is a function of its length l (in feet), given by T(l) = 2pi sq root of l/g, where g = 32.2 feet per second per seconds is the acceleration of gravity. Express the length l as a function of the period T.

If T=2pi*sqrt(l/g) then do the inverse operations to get T in terms of l as
g*(T/(2pi))^2=l

Answer 1

To express the length l as a function of the period T, we can rearrange the equation g*(T/(2pi))^2 = l by multiplying both sides by (2pi)^2 and dividing both sides by g.

First, square both sides of the equation:

(T/(2pi))^2 = l/g

Next, multiply both sides by (2pi)^2:

(2pi)^2 * (T/(2pi))^2 = (2pi)^2 * (l/g)

This simplifies to:

g * (T/(2pi))^2 = l

So, l = g * (T/(2pi))^2

Therefore, the length l is a function of the period T as l(T) = g * (T/(2pi))^2.