The measuring device, as illustrated, suspends the spring under test from the beam (a metal rod) of the physical support structure. A weight is then attached to the lower end of the spring. One end of a 10cm-long enameled wire is stripped and soldered to the center of the bottom surface of the weight plate, while the other end is inserted into water through the central hole of a plate located above the potential sensor. The water level must be high enough to fully submerge the upper plate.
One end of the special transmission cable from the computer-aided teaching system is connected to the A channel of the interface box. At the other end, the short red and black clips (which output ±5V voltage) are connected to the two plates, while the long red clip (the signal terminal) is connected to the beam of the physical bracket. This setup creates an electric field gradient between the two plates. As the spring vibrates, the end of the enameled wire collects the electric field signal in real time, generating a sinusoidal signal.
The measurement principle is based on the stiffness coefficient of the spring, denoted as k, and the suspended mass m. The formula for the vibration period of the spring is given by:
T = 2π√[(m + c·m₀)/k]
where mâ‚€ represents the actual mass of the spring, and c is the ratio of the effective mass to the actual mass. This value, c, is the key parameter being studied.
Next, connect the experimental setup as shown. Gently pull down the load on the spring oscillator so that it moves about 2 cm away from its equilibrium position, then release it to start longitudinal harmonic oscillation.
Using the computer-aided teaching system for data acquisition, the Ut graph is obtained. By using the longitudinal cursor tool in the menu, the vibration period T can be directly read from the graph.
Then, add different loads (standard weights) to the weight plate one by one, making sure the weight plate’s mass is included in the total load. Use the computer again to collect data and record the corresponding vibration periods.
As an example, we have tested both conical and cylindrical springs. Here, we focus on the conical spring.
The improved method offers several advantages. First, it significantly enhances measurement accuracy. Before the improvement, the stopwatch method yielded a c' value of 0.213 ± 0.016, a k' value of 0.941 ± 0.018 N/m, and an r' value of 0.9915. The standard stiffness value k₀ is 0.97 N/m. These results show that the improved method provides more accurate values for c, r, and k.
Second, by converting the elastic force of the vibrating spring into a periodic voltage signal, the method overcomes the challenges of traditional methods like the photogate or stopwatch techniques.
Third, the graphical representation of the spring's motion makes the process visually clear, and the coordinate interception method improves the precision and scientific nature of the period measurement.
Fourth, developing self-made experimental instruments helps students enhance their practical and innovative skills, making this a valuable design experiment for educational purposes.
Finally, this method can also be applied to experiments such as the simple pendulum, compound pendulum, and three-string pendulum, giving it broader applicability and promoting its use in physics education.
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