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Answer :
To solve the problem of finding the length [tex]\( L \)[/tex] of the pendulum, we use the given period equation for a pendulum:
[tex]\[ T = 2 \pi \sqrt{\frac{L}{32}} \][/tex]
We are given:
- The period [tex]\( T = 1.57 \)[/tex] seconds
- [tex]\(\pi = 3.14\)[/tex]
Our goal is to find the length [tex]\( L \)[/tex].
1. Start with the given formula:
[tex]\[ 1.57 = 2 \times 3.14 \times \sqrt{\frac{L}{32}} \][/tex]
2. Simplify the expression by calculating [tex]\( 2 \times 3.14 \)[/tex]:
[tex]\[ 1.57 = 6.28 \times \sqrt{\frac{L}{32}} \][/tex]
3. Divide both sides by 6.28 to isolate the square root:
[tex]\[ \frac{1.57}{6.28} = \sqrt{\frac{L}{32}} \][/tex]
4. Calculate [tex]\(\frac{1.57}{6.28}\)[/tex]:
[tex]\[ \frac{1.57}{6.28} \approx 0.25 \][/tex]
5. Now, we have:
[tex]\[ 0.25 = \sqrt{\frac{L}{32}} \][/tex]
6. Square both sides to eliminate the square root:
[tex]\[ 0.25^2 = \frac{L}{32} \][/tex]
7. Calculate [tex]\( 0.25^2 \)[/tex]:
[tex]\[ 0.25^2 = 0.0625 \][/tex]
8. Multiply both sides by 32 to solve for [tex]\( L \)[/tex]:
[tex]\[ L = 0.0625 \times 32 \][/tex]
9. Calculate [tex]\( 0.0625 \times 32 \)[/tex]:
[tex]\[ L = 2 \][/tex]
So, the length of the pendulum is 2 feet.
[tex]\[ T = 2 \pi \sqrt{\frac{L}{32}} \][/tex]
We are given:
- The period [tex]\( T = 1.57 \)[/tex] seconds
- [tex]\(\pi = 3.14\)[/tex]
Our goal is to find the length [tex]\( L \)[/tex].
1. Start with the given formula:
[tex]\[ 1.57 = 2 \times 3.14 \times \sqrt{\frac{L}{32}} \][/tex]
2. Simplify the expression by calculating [tex]\( 2 \times 3.14 \)[/tex]:
[tex]\[ 1.57 = 6.28 \times \sqrt{\frac{L}{32}} \][/tex]
3. Divide both sides by 6.28 to isolate the square root:
[tex]\[ \frac{1.57}{6.28} = \sqrt{\frac{L}{32}} \][/tex]
4. Calculate [tex]\(\frac{1.57}{6.28}\)[/tex]:
[tex]\[ \frac{1.57}{6.28} \approx 0.25 \][/tex]
5. Now, we have:
[tex]\[ 0.25 = \sqrt{\frac{L}{32}} \][/tex]
6. Square both sides to eliminate the square root:
[tex]\[ 0.25^2 = \frac{L}{32} \][/tex]
7. Calculate [tex]\( 0.25^2 \)[/tex]:
[tex]\[ 0.25^2 = 0.0625 \][/tex]
8. Multiply both sides by 32 to solve for [tex]\( L \)[/tex]:
[tex]\[ L = 0.0625 \times 32 \][/tex]
9. Calculate [tex]\( 0.0625 \times 32 \)[/tex]:
[tex]\[ L = 2 \][/tex]
So, the length of the pendulum is 2 feet.
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