Simple Pendulum

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Approximate length of simple pendulum with period 2 s (g=10 m/s²)?

RankGuru · Accepted Answer

1. **Fundaμental Formula**: The period of a simple pendulum for small oscillations is $T = 2\pi \sqrt{\frac{L}{g}}$.
2. **Given**: $T = 2$ s and $g = 10 	ext{ m/s}^2$.
3. **Isolate Length (L)**:
   - $2 = 2\pi \sqrt{\frac{L}{10}}$
   - $1 = \pi \sqrt{\frac{L}{10}}$
   - $\frac{1}{\pi} = \sqrt{\frac{L}{10}} \implies \frac{1}{\pi^2} = \frac{L}{10}$.
4. **Numerical Approximation**: Since $\pi^2 \approx 9.87 \approx 10$:
   - $L \approx \frac{10}{10} = 1.0$ m.
5. **Note**: A pendulum with a period of exactly $2$ seconds is called a **Seconds Pendulum**.

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Simple Pendulum

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