Value of g using slope of T²vs L

 Finding g using T² vs L Graph

1. Set up a simple pendulum with a known string length (L) and a small bob.

2. Measure the time (T) for 20 oscillations and divide by 20 to get the time period.

3. Change the length and repeat to get multiple values of T² and L.

4. Plot a graph of T² (Y-axis) vs L (X-axis).

5. A straight line through the origin confirms that T² ∝ L.

6. Find the slope of the line: Slope = T² / L.

7. Use the formula: g = 4π² / slope to calculate acceleration due to gravity.

Example Calculation:

• Choose points: (0.25, 1.00) and (1.00, 4.00)

• Slope (m) = (y2-y1)/(x2-x1): (4.00 - 1.00) / (1.00 - 0.25) = 3.0 / 0.75 = 4.0

• Calculating g: g = 4π² / slope = 4 × (3.14159)² / 4.0 = 9.87 m/s²

Got a doubt? Curious about pendulums or graphs?

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