Question

The period T (in seconds) of a pendulum is given by T=2\pi \sqrt((L)/(32)), where L stands for the length (in feet) of the pendulum. If \pi =3.14, and the period is 1.57 seconds, what is the length?

Answer 1

The first thing we must do in this case is to rewrite the equation correctly:
 T = 2 * pi * root (l / 32)
 From here, we clear l:
 T / (2 * pi) = root (l / 32)
 l / 32 = (T / (2 * pi)) ^ 2
 l = 32 * (T / (2 * pi)) ^ 2
 Substituting values:
 l = 32 * (1.57 / (2 * 3.14)) ^ 2
 l = 2 feet
 Answer:
 the length is:
 l = 2 feet