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 3.14 seconds, what is the length?
16 feet
80 feet
32 feet
8 feet

Explanation:

Step1: Substitute given values

Given $T = 3.14$, $\pi=3.14$ into $T = 2\pi\sqrt{\frac{L}{32}}$, we get $3.14 = 2\times3.14\sqrt{\frac{L}{32}}$.

Step2: Simplify the equation

First, divide both sides by $2\times3.14$. So, $\frac{3.14}{2\times3.14}=\sqrt{\frac{L}{32}}$, which simplifies to $0.5=\sqrt{\frac{L}{32}}$.

Step3: Square both sides

Squaring both sides gives $(0.5)^2=\frac{L}{32}$, so $0.25=\frac{L}{32}$.

Step4: Solve for L

Multiply both sides by 32, $L = 0.25\times32=8$.

Answer:

8 feet