The measuring device, as illustrated, suspends the spring under test from the beam (a metal rod) of the physical support. A weight is attached to the lower end of the spring. One end of a 10 cm long enameled wire is stripped, and the insulating paint is welded to the center of the bottom surface of the weight plate. The other end of the wire is inserted into water through the central hole of a plate located above the potential sensor. The water level must be sufficient to submerge the upper plate.
One end of the special transmission line 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 (signal end) 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 endpoint of the enameled wire collects the electric field signal in real time, generating a sinusoidal waveform.
The measurement principle relies on the formula for the vibration period of a spring:
T = 2π√[(m + c·m₀)/k]
where k is the spring stiffness coefficient, m is the suspended mass, mâ‚€ is the actual mass of the spring, and c is the ratio of the effective mass to the actual mass. The goal is to determine the value of c.
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, data is collected to obtain the Ut graph. By using the longitudinal strip cursor in the menu, the vibration period T can be measured accurately.
Then, add different masses (standard weights) to the weight plate one by one (including the mass of the weight plate itself), and use the computer to collect data again to measure the corresponding vibration periods.
As an example, we have studied both conical and cylindrical springs. Here, we take the conical spring as a case study.
The improved method offers several advantages. First, it significantly improves measurement accuracy. Before the improvement, using the stopwatch method, the results were: c' = 0.213 ± 0.016, k' = 0.941 ± 0.018 N/m, r' = 0.9915. The standard value of the spring stiffness coefficient k₀ is 0.97 N/m. The measured values of c, r, and k demonstrate that the improvement enhances accuracy.
Second, by converting the elastic force of the vibrating spring into a varying voltage signal, the vibration period can be measured more easily than with traditional methods like photogates or stopwatches.
Third, the graphical method provides a clear and visual representation of the spring’s motion, and the coordinate interception technique makes the period measurement more accurate and scientific.
Fourth, developing self-made experimental equipment helps students improve 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 simple pendulums, compound pendulums, and three-string pendulums, showing its broad applicability and potential for wider adoption.
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