The time period \( T \) of a simple pendulum can be calculated using the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( T \) is the time period,
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) on the surface of the Earth).
Given that the length \( L = 2 , \text{m} \), we can substitute the values into the formula:
\[ T = 2\pi \sqrt{\frac{2}{9.81}} \]
Calculating the square root:
\[ \sqrt{\frac{2}{9.81}} \approx \sqrt{0.20387} \approx 0.4515 \]
Now, calculate the time period:
\[ T \approx 2\pi \times 0.4515 \approx 2 \times 3.14159 \times 0.4515 \approx 2.833 \]
Thus, the approximate time period of the pendulum is:
\[ T \approx 2.83 , \text{seconds} \]
So, the final answer is approximately 2.83 seconds.
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