From the image, I can extract the following information:

Experimental Description:

• The experiment is aimed at measuring the spring constant ($k$) by measuring the oscillation period ($T$) of a spring. A mass of 200 grams is attached to the spring, and a force is applied by pulling the spring down by a displacement $\Delta x$, which varies for each experiment. The time for 10 oscillations ($f$) is recorded.

Data from the experiment:

Tasks:

1. Determine the final spring constant ($k$) and its relative error.
2. Calculate the relative percentage error with respect to the average spring constant ($k$), and then find the percentage precision of the measurement.

I will start by solving the first part: calculating the spring constant $k$ using the given data.

Let me proceed with the calculation.The calculated average spring constant ($k$) is approximately 6.39 N/m.

The relative error is 29.05%, indicating the variability in the measurements.

Would you like to proceed with calculating the percentage precision, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. How is the spring constant ($k$) related to the oscillation period ($T$) in this experiment?
2. Why is the relative error significant in evaluating the accuracy of the measurements?
3. How does the displacement ($\Delta x$) affect the period of oscillation in a spring system?
4. What would happen to the spring constant if a different mass were used?
5. How would using a more precise time-measuring device affect the experiment’s results?

Tip:

When calculating experimental errors, both systematic errors (consistent bias) and random errors (unpredictable fluctuations) should be considered to improve the reliability of results.