We appreciate your visit to The movement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer The period. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We are given the formula for the period of a pendulum:
[tex]$$
T = 2\pi \sqrt{\frac{L}{32}},
$$[/tex]
where:
- [tex]$T$[/tex] is the period (in seconds),
- [tex]$\pi = 3.14$[/tex] (approximation), and
- [tex]$L$[/tex] is the length of the pendulum (in feet).
Given that [tex]$T = 1.57$[/tex] seconds, we need to solve for [tex]$L$[/tex]. Follow these steps:
1. Substitute the given value into the equation:
[tex]$$
1.57 = 2 \cdot 3.14 \cdot \sqrt{\frac{L}{32}}.
$$[/tex]
2. Simplify the constant term:
Compute [tex]$2 \cdot 3.14$[/tex]:
[tex]$$
2 \cdot 3.14 = 6.28.
$$[/tex]
Now the equation becomes:
[tex]$$
1.57 = 6.28 \sqrt{\frac{L}{32}}.
$$[/tex]
3. Isolate the square root term:
Divide both sides by [tex]$6.28$[/tex]:
[tex]$$
\sqrt{\frac{L}{32}} = \frac{1.57}{6.28}.
$$[/tex]
Notice that:
[tex]$$
\frac{1.57}{6.28} = 0.25.
$$[/tex]
4. Eliminate the square root by squaring both sides:
[tex]$$
\left(\sqrt{\frac{L}{32}}\right)^2 = (0.25)^2,
$$[/tex]
which simplifies to:
[tex]$$
\frac{L}{32} = 0.0625.
$$[/tex]
5. Solve for [tex]$L$[/tex]:
Multiply both sides by [tex]$32$[/tex]:
[tex]$$
L = 32 \times 0.0625.
$$[/tex]
Calculating this:
[tex]$$
L = 2.
$$[/tex]
Thus, the length of the pendulum is [tex]$\boxed{2\ \text{feet}}$[/tex].
[tex]$$
T = 2\pi \sqrt{\frac{L}{32}},
$$[/tex]
where:
- [tex]$T$[/tex] is the period (in seconds),
- [tex]$\pi = 3.14$[/tex] (approximation), and
- [tex]$L$[/tex] is the length of the pendulum (in feet).
Given that [tex]$T = 1.57$[/tex] seconds, we need to solve for [tex]$L$[/tex]. Follow these steps:
1. Substitute the given value into the equation:
[tex]$$
1.57 = 2 \cdot 3.14 \cdot \sqrt{\frac{L}{32}}.
$$[/tex]
2. Simplify the constant term:
Compute [tex]$2 \cdot 3.14$[/tex]:
[tex]$$
2 \cdot 3.14 = 6.28.
$$[/tex]
Now the equation becomes:
[tex]$$
1.57 = 6.28 \sqrt{\frac{L}{32}}.
$$[/tex]
3. Isolate the square root term:
Divide both sides by [tex]$6.28$[/tex]:
[tex]$$
\sqrt{\frac{L}{32}} = \frac{1.57}{6.28}.
$$[/tex]
Notice that:
[tex]$$
\frac{1.57}{6.28} = 0.25.
$$[/tex]
4. Eliminate the square root by squaring both sides:
[tex]$$
\left(\sqrt{\frac{L}{32}}\right)^2 = (0.25)^2,
$$[/tex]
which simplifies to:
[tex]$$
\frac{L}{32} = 0.0625.
$$[/tex]
5. Solve for [tex]$L$[/tex]:
Multiply both sides by [tex]$32$[/tex]:
[tex]$$
L = 32 \times 0.0625.
$$[/tex]
Calculating this:
[tex]$$
L = 2.
$$[/tex]
Thus, the length of the pendulum is [tex]$\boxed{2\ \text{feet}}$[/tex].
Thanks for taking the time to read The movement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer The period. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
