To determine the percentage error observed by Kowan and Lupe in measuring the pendulum’s oscillation, we need to:

1. Calculate the theoretical period of a pendulum using the formula: $T = 2\pi \sqrt{\frac{L}{g}}$ where:

   • $L = 88 \, \text{cm} = 0.88 \, \text{m}$ (length of the pendulum),
   • $g = 9.8 \, \text{m/s}^2$ (acceleration due to gravity),
   • $T$ is the period of one oscillation.

2. Calculate the experimental period from Lupe's timing: $T_{\text{exp}} = \frac{21.85 \, \text{s}}{12} = 1.8208 \, \text{s}$

3. Calculate the theoretical period: $T = 2\pi \sqrt{\frac{0.88}{9.8}}$ Performing this calculation, we get $T \approx 1.884 \, \text{s}$.

4. Determine the percentage error using the formula: $\text{Percentage Error} = \left| \frac{T_{\text{exp}} - T}{T} \right| \times 100$ Substituting values: $\text{Percentage Error} = \left| \frac{1.8208 - 1.884}{1.884} \right| \times 100$ $\approx \left| \frac{-0.0632}{1.884} \right| \times 100 \approx 3.4\%$

Answer: The percentage error observed by Kowan and Lupe is approximately 3.4%.

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Related Questions

1. How would the percentage error change if the length measurement was 1 cm shorter?
2. How does the period of a pendulum depend on the acceleration due to gravity?
3. If the timing was only for 6 oscillations, how would that affect the percentage error?
4. What is the effect of measuring the length in inches instead of centimeters?
5. How could the percentage error be minimized with more accurate timing methods?

Tip

When measuring multiple oscillations and averaging, minor timing inaccuracies have less impact on each individual oscillation's period.