A student investigated the damping of a rotational pendulum using the apparatus shown - Edexcel - A-Level Physics - Question 3 - 2023 - Paper 6

1. Calculate ln θ values based on the maximum displacement angles given:

   • For n = 10, θ = 124: ln(124) ≈ 4.820
   • For n = 20, θ = 82: ln(82) ≈ 4.406
   • For n = 30, θ = 55: ln(55) ≈ 3.989
   • For n = 40, θ = 37: ln(37) ≈ 3.610
   • For n = 50, θ = 25: ln(25) ≈ 3.219
   • For n = 60, θ = 16: ln(16) ≈ 2.773

2. Create a table with the calculated ln θ values.

3. Plot these points on the provided grid with appropriate axes labeled: the x-axis as n and the y-axis as ln θ.

4. Ensure to draw a best-fit line that approximates the plotted points.

1. Identify two points on the best-fit line from the graph to determine the gradient. Select points (n₁, ln θ₁) and (n₂, ln θ₂).

2. Use the gradient formula: ext{Gradient} = rac{(ln heta_2 - ln heta_1)}{(n_2 - n_1)}

3. Given that the gradient is -λ, take the negative of the calculated gradient to find λ: $λ = - ext{Gradient}$

To assess the student's claim, we must determine θ₀ from the equation rearranged:

$ext{ln}( heta) = ext{ln}( heta_0) - λn$

At n = 0, we have θ = θ₀. By calculating the y-intercept of the best-fit line and using the rearranged equation:

θ₀ can be determined; if θ₀ > 180°, the claim is correct. Conversely, if θ₀ ≤ 180°, the claim is false.