Question

the period t (in seconds) of a pendulum is given by t = 2π√(l/32), where l stands for the length (in feet) of the pendulum. if π = 3.14, and the period is 15.7 seconds, what is the length of the pendulum? the length of the pendulum is ____ feet. the solution is

Explanation:

Step1: Substitute given values into formula

Given $T = 15.7$, $\pi=3.14$ into $T = 2\pi\sqrt{\frac{L}{32}}$. So, $15.7=2\times3.14\sqrt{\frac{L}{32}}$.

Step2: Simplify the right - hand side

$2\times3.14 = 6.28$, so the equation becomes $15.7 = 6.28\sqrt{\frac{L}{32}}$.

Step3: Solve for $\sqrt{\frac{L}{32}}$

Divide both sides of the equation by $6.28$: $\frac{15.7}{6.28}=\sqrt{\frac{L}{32}}$. Since $\frac{15.7}{6.28}=2.5$, we have $2.5=\sqrt{\frac{L}{32}}$.

Step4: Square both sides

$(2.5)^2=\frac{L}{32}$. So, $6.25=\frac{L}{32}$.

Step5: Solve for $L$

Multiply both sides by 32: $L=6.25\times32 = 200$.

Answer:

200