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courses:phy101l:2

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2. Gravitational acceleration from a pendulum

1. Introduction and theory

For a simple pendulum

$$ T = 2\pi \sqrt{\frac{L}{g}} \Rightarrow g = 4\pi^2 \frac{L}{T^2}. $$

For a compound pendulum

$$ T = 2\pi \sqrt{\frac{\frac{K^2}{l}+l}{g}} $$

and, hence, a compound pendulum is equivalent to a simple pendulum if

$$ L = \frac{K^2}{l} + l \Rightarrow l^2 - lL + K^2 = 0 $$

which is a quadratic equation with two solutions $l_1$ and $l_2$ where $l_1+l_2=L$ and $l_1l_2=K^2$.

You have to find gravitational acceleration $g$ and radius of gyration $K=\sqrt{l_1l_2}$.

2. Method and data

2.1 Data table

Hole no. Distance [cm] Trial Time for 10 oscillations [s]
1 10 1
2
2 20 1
2
3 30 1
2
4 40 1
2
6 60 1
2
7 70 1
2
8 80 1
2
9 90 1
2

3. Graphical analysis

4. Results

5. Discussion and conclusion

courses/phy101l/2.1687019402.txt.gz · Last modified: by asad

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