In the demonstration performed by the 8th Period class, Kowan measure the length of the pendulum to be 88 cm, and Lupe time the 12 oscillations and obtained a total time of 21.85 seconds. QUESTION: Determine the percentage error  observed by Kowan and Lupe. One decimal point number only

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%**.

Would you like further details or have any questions?

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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.

In the demonstration performed by the 8th Period class, Kowan measure the length of the pendulum to be 88 cm, and Lupe time the 12 oscillations and obtained a total time of 21.85 seconds. QUESTION: Determine the percentage error observed by Kowan and Lupe. One decimal point number only.

Determine the percentage error in the pendulum motion experiment conducted by Kowan and Lupe. Using the theoretical and experimental periods, this problem involves key concepts in periodic motion and error analysis. Suitable for students in Grades 9-12.

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