An experiment needs to test a hypothesis. One trick in intro physics is to find a hypothesis that is interesting and not trivial. Another trick is designing an experiment with good accuracy given the available materials. One thing I've noticed over the years is how easy it is to accurately measure time and frequency with the Vernier-type data collectors available in many intro labs, but how much harder it is to accurately measure quantities that are more related to the input amplitude (voltage, temperature, force, sound level, pH, etc.)
Therefore, if have a Vernier-type device available and you want accuracy to be a strong selling point for your experiment, test a hypothesis that strongly relates to time (period) or frequency and only weakly relates to amplitudes that are harder to measure more accurately than 1-2%. Those Vernier-type devices can easily measure time and frequency to 0.01-0.1% with a good design and a little care.
An example of an experiment exploiting this strength might be to test the formulas (see:
https://en.wikipedia.org/wiki/Pendulum ) relating how the period of a simple pendulum depends on its initial angle of oscillation. If you let T0 be the period of the pendulum with true very small angles, then you can relate T(theta) to it for other initial angles without fumbling about with the accuracy of your length and g estimates (as long as they are constant). Teachers tend to be impressed with experimental designs that succeed in accurately measuring very small differences.
A few tips on this experiment:
1. I would hang the pendulum from a force sensor and sample the rate as fast as possible to measure the period.
2. I would suspend the pendulum from a braided fishing line (20-40 lb power pro or similar) to ensure a constant length. Temperature and humidity of the room need to be approximately constant over the experimental period.
3. The length of the pendulum is a balance between the number of cycles you want to measure over and how much data the digitizer can store. I would tend to want to sample for 10-20 cycles.
4. Define your period as twice the time interval from peak force to peak force. Fitting 10-20 data points near the peak to a quadratic will determine the true time of the peak more accurately than inspecting for the single point with the largest force.
5. You need a mass (pendulum bob) heavy and small enough that you can neglect air resistance, yet light enough that you can completely ignore stretch in the string and stretch in the sensor. You do not want your peak angle changing over the 10-20 cycles of each measurement.
Lots of other very accurate experiments are possible with Verniers and with the sound cards built into most computers. Last year, I mentored an elementary school student in a science project using Audacity to study the effects of changing temperature on the frequency of a guitar string. The frequency changes are small, but Audacity and a sound card allow for measuring them very accurately (compared with most school physics lab capabilities.)