Question

the period (t) (in seconds) of a pendulum is given by (t = 2pisqrt{\frac{l}{32}}), where (l) stands for the length (in feet) of the pendulum. if (pi=3.14), and the period is 6.28 seconds, what is the length?
32 feet
6.4 feet
64 feet
3.2 feet

Explanation:

Step1: Substitute given values into formula

Given $T = 2\pi\sqrt{\frac{l}{32}}$, $T = 6.28$ and $\pi=3.14$. Substitute these values: $6.28 = 2\times3.14\sqrt{\frac{l}{32}}$.

Step2: Simplify the right - hand side

$2\times3.14 = 6.28$, so the equation becomes $6.28=6.28\sqrt{\frac{l}{32}}$. Divide both sides by $6.28$: $\frac{6.28}{6.28}=\sqrt{\frac{l}{32}}$, which simplifies to $1=\sqrt{\frac{l}{32}}$.

Step3: Square both sides to solve for $l$

Squaring both sides gives $1^2=\frac{l}{32}$, so $l = 32$.

Answer:

32 feet