An experimental device for measuring gravitational acceleration using a single pendulum and an atomic clock

Abstract

The utility model provides an experimental device that will atomic clock be used for simple pendulum measurement gravity acceleration, including rudder machine, drive rod electromagnet, support frame, pendulum ball, base, visual identification system, atomic clock, be provided with support component on the base, rudder machine, pendulum ball all set up in support component, the output shaft of rudder machine is connected electromagnet through drive rod, electromagnet corresponds with pendulum ball, visual identification system is aligned pendulum ball, atomic clock is used for simple pendulum period measurement. Will atomic clock be used for simple pendulum measurement, can reduce the error brought in period measurement, through atomic clock module and electromagnet trigger's hardwiring connection structure, control period measurement error in <=10mu s, reduce 98% or above than traditional photoelectric gate device error, thereby reduce the error brought in data measurement, provide more reliable data for the calculation of gravity acceleration. Modular design simplifies installation debugging process, and low power consumption and heat dissipation design guarantee the stability of equipment operation.

Description

Technical Field

[0001] This utility model relates to the field of atomic clock application technology, specifically an experimental device for using an atomic clock to measure gravitational acceleration using a pendulum. Background Technology

[0002] In the field of physics, the simple pendulum experiment, as a classic experiment for measuring gravitational acceleration and studying simple harmonic motion, holds a crucial position and has been widely used in teaching and research since the time of Galileo.

[0003] Currently, traditional pendulum experiments generally use relatively basic apparatus, typically consisting of a pendulum string, a small ball, a timer (such as a stopwatch), a steel tape measure, and vernier calipers. During operation, the experimenter must manually measure the pendulum length and record data such as the oscillation period. A study by students at Huangpi No. 1 Middle School using an innovative experimental apparatus for pendulum experiments mentions that high school physics textbooks have long relied on such basic apparatus for pendulum experiments. Due to time constraints in experimental courses, students must complete multiple steps in a short period, and many aspects rely on visual observation, such as determining the position of the ball's swing and the start and end times. This easily introduces human error, leading to significant deviations between experimental results and true values.

[0004] From the perspective of measurement accuracy, traditional methods have many shortcomings: the reaction time difference of manual timing leads to large errors in period measurement; when measuring pendulum length with a steel tape measure, the repeatability is poor and systematic errors are easily generated due to different measurement points and methods. In addition, the uneven distribution of the pendulum bob's mass will cause it to rotate during the swing, resulting in a change in the actual pendulum length, which in turn affects the oscillation period; the tension of the pendulum string is affected by the weight of the pendulum bob and the vibration, and its changes will also cause fluctuations in the oscillation period.

[0005] In terms of experimental setup, the traditional simple pendulum experimental setup also has obvious design flaws. As mentioned in the improvement of the experimental setup for the experiment "Exploring Factors Affecting the Period of a Simple Pendulum," the traditional setup consists of an iron stand, a thin rope, and a small steel ball, which suffers from poor intuitiveness and large measurement errors: the pendulum angle cannot be quantitatively displayed, making it difficult to control within the experimental requirements; it is not easy to determine whether the pendulum moves in the same vertical plane, and if the ball moves in a conical pendulum motion, it will seriously affect the experimental results; the equilibrium position is difficult to determine accurately, which brings difficulties to the measurement. The discussion on the improvement of the simple pendulum apparatus in university physics experiments mentions that some commonly used simple pendulum apparatuses lack a vertical scale, making it inconvenient to read the pendulum length, and repeated measurements with a ruler can easily damage the pendulum string; some lack a horizontal scale, requiring remeasurement of the pendulum amplitude for each swing; most do not have an angle measuring device, requiring recalculation of the pendulum angle when the pendulum length changes; and some instruments are not equipped with a level, which can easily result in a conical pendulum if not leveled, affecting the experimental effect and progress.

[0006] Furthermore, environmental factors significantly interfere with traditional pendulum experiments. Fluctuations in ambient temperature and humidity cause thermal expansion and contraction of the pendulum string material, as well as moisture absorption and deformation, resulting in subtle changes in the pendulum length. Changes in air pressure also alter the magnitude of air resistance on the pendulum's oscillation, affecting its damping characteristics. These environmental variables make it difficult to reproduce consistent results in experiments conducted under different temporal and spatial conditions, severely limiting the stability of experimental data and the reproducibility of scientific research.

[0007] To address the shortcomings of traditional pendulum experiments, some research has attempted to improve experimental setups using new technologies. For example, some middle schools in China have tried using mobile phone sensors combined with Phyphox to conduct pendulum experiments. Data is collected using the phone's built-in sensors, and algorithms are used to calculate the oscillation period and gravitational acceleration, greatly simplifying the experimental process. However, limitations in the accuracy of mobile phone sensors result in significant errors when measuring minute oscillation angles. Laboratories in Europe and America widely use high-definition industrial cameras combined with computer vision algorithms to achieve dynamic monitoring and non-contact measurement of oscillation angles, but face challenges such as complex image processing algorithms and high costs. Furthermore, some research institutions use high-precision measuring instruments such as laser interferometers, which can achieve sub-micron level measurement accuracy, but the equipment is expensive and has a high operational threshold, making it difficult to promote in basic teaching scenarios. While these new technologies improve experimental accuracy and automation, they still suffer from high costs, incomplete functionality, inconvenient operation, and insufficient adaptability to teaching, making them difficult to widely apply in physics experiments in primary, secondary, and tertiary schools, as well as in scientific research and industrial measurement.

[0008] In summary, traditional pendulum experiments and apparatus have significant shortcomings in terms of ease of operation, measurement accuracy, and universality of teaching and application. There is an urgent need for a new experimental system to overcome these problems, realize the automation, precision, and intelligence of pendulum experiments, and provide strong support for the reform of physics experiment teaching and scientific research applications. Utility Model Content

[0009] (a) Technical problems to be solved

[0010] To address the shortcomings of existing technologies, this invention provides an experimental device for using an atomic clock to measure gravitational acceleration using a simple pendulum, thus solving the problems mentioned in the background section.

[0011] (II) Technical Solution

[0012] To achieve the above objectives, this utility model is implemented through the following technical solution: an experimental device for measuring gravitational acceleration using an atomic clock in a pendulum, comprising a servo motor, a drive rod electromagnet, a support frame, a pendulum bob, a base, a visual recognition system, and an atomic clock. The base is provided with a support component, and the servo motor and pendulum bob are both mounted on the support component. The output shaft of the servo motor is connected to the electromagnet through the drive rod. The electromagnet corresponds to the pendulum bob. The visual recognition system is aligned with the pendulum bob, and the atomic clock is used for measuring the period of the pendulum.

[0013] Preferably, the support component includes a servo clamp, a support frame, and a support rod. The support rod is vertically mounted on the base, the support frame is mounted on top of the support rod, the servo clamp is mounted on the support frame and is used to fix the servo, and the pendulum ball is fixed to the support frame by a connecting rope.

[0014] Preferably, the atomic clock is a miniaturized, traceable rubidium atomic clock module.

[0015] Preferably, the visual recognition system includes a camera bracket and a high-definition camera mounted on the camera bracket, the high-definition camera being aimed at the pendulum ball.

[0016] Preferably, a background plate is provided behind the electromagnet and the pendulum.

[0017] (III) Beneficial Effects

[0018] This invention provides an experimental device for using an atomic clock to measure gravitational acceleration using a simple pendulum.

[0019] It has the following beneficial effects:

[0020] 1. This experimental device uses an atomic clock to measure gravitational acceleration using a simple pendulum. Applying an atomic clock to pendulum measurements reduces errors in period measurement. Through a hardwired connection between the atomic clock module and the electromagnet trigger, the period measurement error is controlled to ≤10μs, reducing the error by more than 98% compared to traditional photoelectric gate devices. This reduces errors in data measurement and provides more reliable data for calculating gravitational acceleration. The modular design simplifies the installation and debugging process, while low power consumption and heat dissipation design ensure stable operation. Attached Figure Description

[0021] Figure 1 This is an isometric view of the present invention;

[0022] Figure 2 This is a schematic diagram of the supporting component structure of this utility model.

[0023] In the diagram: 1. Servo clamp, 2. Servo, 3. Drive rod, 4. Electromagnet, 5. Support frame, 6. Pendulum, 7. Connecting rope, 8. Background plate, 9. Base, 10. Base cover, 11. Main control unit, 12. Atomic clock, 13. High-definition camera, 14. Camera bracket, 15. Support rod. Detailed Implementation

[0024] This invention provides an experimental device for measuring gravitational acceleration using an atomic clock in a pendulum. By integrating mechanical structure, electromagnetic control, visual acquisition, and intelligent computing modules, it achieves precise control, dynamic acquisition, and data analysis of the pendulum's motion.

[0025] Specifically, such as Figure 1-2 As shown, the experimental setup includes a servo motor 2, a drive rod 3, an electromagnet 4, a support frame 5, support components, a pendulum ball 6, a base 9, a visual recognition system, and an atomic clock 12.

[0026] The supporting components include a servo clamp 1, a support frame 5, and a support rod 15. The support rod 15 is vertically mounted on the base 9, and the support frame 5 is positioned on top of the support rod 15. The servo clamp 1 is mounted on the support frame 5 and is used to fix the servo 2. The servo clamp 1 has a mounting slot for accommodating the servo 2, and the servo 2 is installed in the mounting slot. To improve the stability of the servo clamp 1, a thermoplastic nut is embedded at the top of the servo clamp 1, and a sufficiently long screw is screwed in to firmly fix the servo clamp 1 to the support frame 5. The pendulum 6 is fixed to the support frame 5 by a connecting rope 7. The pendulum 6 hangs naturally. As the core moving body of the experiment, the pendulum 6 uses a metal ball of uniform density to ensure stable motion inertia.

[0027] Servo motor 2 is used to control the initial swing angle of pendulum ball 6, supporting program-set swing angles to achieve standardized swing initiation; one end of drive rod 3 is fixed to the output shaft of servo motor 2, and drive rod 3 hangs down to the arc-shaped motion trajectory of pendulum ball 6, while the other end of drive rod 3 is connected to electromagnet 4. Electromagnet 4 is optionally equipped with a magnetic release function, which replaces the servo motor in initiation and is used to attract and release pendulum ball 6 to achieve free swing triggering. Electromagnet 4 corresponds to pendulum ball 6. By rotating servo motor 2, the electromagnet 4 that attracts pendulum ball 6 is driven to a suitable position, giving pendulum ball 6 initial potential energy and precisely controlling the swing initiation state.

[0028] The visual recognition system is aligned with the pendulum ball 6. The visual recognition system includes a camera bracket 14 and a high-definition camera 13 mounted on the camera bracket 14. The high-definition camera 13 is aligned with the pendulum ball 6. The high-definition camera 13 captures images of the pendulum ball's motion at a frame rate of ≥60fps with a resolution of 1080p, and supports HSV color segmentation and contour recognition.

[0029] The base 9 supports the mechanical structure and electronic modules, ensuring the overall stability of the device. A base cover 10 is installed on the base 9 to protect the internal electronic components, conceal wiring, improve aesthetics, and provide ventilation holes and wiring channels. The base 9 houses the ESP32 main control unit 11, which integrates WiFi / Bluetooth communication and controls the servo motor 2 and electromagnet 4, receiving and initially processing data from the high-definition camera 13. The main control unit 11, or an independently configured switching circuit, selectively enables or bypasses the atomic clock module. In enabled mode, the atomic clock module is used for high-precision period measurement; in comparison mode, it switches to a conventional timer, either built-in or external. This function is specifically designed for educational purposes, visually demonstrating the errors introduced by atomic clock timing technology.

[0030] A background plate 8 is located behind the electromagnet 4 and the pendulum ball 6. The background plate 8 is used to provide a high-contrast visual background, assist the high-definition camera 13 in recognizing the outline of the pendulum ball, and reduce environmental interference.

[0031] Atomic clock 12 is used for measuring the period of a simple pendulum. Atomic clock 12 provides a high-precision time reference, synchronizes camera acquisition with motion control timing, ensures data timing consistency, and improves measurement accuracy. For ease of installation and maintenance, atomic clock 12 preferably employs a miniaturized, traceable rubidium atomic clock module and a bracket that works with it. The bracket has pre-drilled threaded holes. The atomic clock module is securely mounted to the bracket with screws, and the bracket is then fixed to the pendulum body. To reduce power consumption and adapt to experimental environments, the atomic clock module uses a miniaturized package, controlling power consumption to the level of hundreds of milliwatts to several watts, facilitating teaching applications.

[0032] It also includes a heat dissipation device for cooling the atomic clock module (20). The heat dissipation device can be a small cooling fan to maintain the operating temperature of the atomic clock module and ensure its accuracy and stability.

[0033] In the standardized pendulum period measurement experiment, mechanical assembly is performed first. The servo motor 2 is fixed to the servo motor fixture 1, and the drive rod 3 is adjusted to connect with the pendulum bob 6, ensuring that the pendulum bob 6 is aligned with the center of the background plate 8 when it is vertically stationary. The lens of the high-definition camera 13 is aimed at the plane of motion of the pendulum bob 6, and the focal length is adjusted to obtain a clear image of the pendulum bob. Then, the electronic system is initialized by connecting the ESP32 main control unit 11, the atomic clock 12, the high-definition camera 13, and the power supply. The computer or mobile phone is connected via Micro-USB or WiFi. The experimental control program is then opened, and the parameters are configured: pendulum length L, sampling frame rate, number of experiments, and enabling "HSV color segmentation + Gaussian blur" preprocessing, and setting the pendulum bob color threshold.

[0034] After preparation, the initial swing angle is set, and the program sends a command to the main control unit 11 to control the servo motor 2 to rotate, driving the electromagnet 4 to deflect to the target angle and energize it to attract the pendulum bob 6 to the initial position. Then, the electromagnet 4 is de-energized, triggering the pendulum bob 6 to swing freely. The atomic clock 12 synchronously triggers the high-definition camera 13 to acquire images at 60fps. The high-definition camera 13 transmits the images to the main control unit 11 in real time. The outline of the pendulum bob 6 is extracted through HSV color segmentation, and after Gaussian blur noise reduction, the centroid coordinates are calculated. The outline of each frame is extracted using `cv2.findContours`, and the centroid is calculated using `cv2.moments`. If there is occlusion, the centroid of the previous frame is used for backtracking. The program identifies the time difference (atomic clock timestamp) between two consecutive times the pendulum bob 6 passes through the lowest point, calculates the period T, repeats this process 5 times and takes the average, and finally, the gravitational acceleration g is calculated back according to the simple pendulum formula, and the result is output. The test was conducted in a laboratory under constant temperature (25℃±1℃), in the dark (background illumination uniformity >95%), using a high-definition camera with a resolution of 1920×1080 and an atomic clock with an accuracy of 10. - 6 Under test conditions of s, ESP329 operation frequency of 240MHz, and repeated experiments, the measurement results meet the experimental accuracy requirements. Furthermore, the combination of HSV color segmentation and machine learning anti-interference enables the pendulum ball 6 recognition success rate to be >98%, effectively supporting digital measurement.

[0035] This example also conducted anti-interference verification under complex environments, simulating complex interference in the field or teaching laboratory. Fluorescent lamp flickering was used to simulate illumination interference (frequency 50Hz, brightness fluctuation ±20%); random texture stickers were pasted on background board 8 to simulate a non-uniform background, and background interference was verified through experiments; slight vibrations (amplitude 1mm, frequency 2Hz) were applied to base 9 to simulate motion interference. To improve the accuracy of the results, this example implemented anti-interference strategies. A "isolated forest + random forest" machine learning model was used to train 1000 sets of interference image data, identifying abnormal frames (such as contour distortion caused by sudden changes in illumination) to optimize the algorithm; "environmental calibration" was performed before the experiment to automatically optimize the HSV threshold and Gaussian kernel parameters. Comparing the periodic errors before and after optimization, it was found that through visual algorithms and dynamic calibration, the device's periodic measurement error in complex environments was <0.3%, meeting the requirements of field and teaching scenarios.

[0036] In summary, this device achieves digitization, standardization, and interference-resistant measurement of the pendulum experiment through the coordinated use of "mechanical control (servo motor 2, electromagnet 4) + visual acquisition (high-definition camera 13) + intelligent algorithms (HSV segmentation, machine learning) + high-precision timing (atomic clock 12)". It is adaptable to diverse scenarios from the laboratory to the field, and after testing, the cycle error is <0.5% and the g-value measurement accuracy is <0.2%, making it a standardized device for physics teaching and scientific research measurements.

[0037] Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the present invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An experimental apparatus for using an atomic clock to measure gravitational acceleration using a simple pendulum, characterized in that: The system includes a servo motor (2), a drive rod (3), an electromagnet (4), a support frame (5), a pendulum (6), a base (9), a vision recognition system, and an atomic clock (12). The base (9) is equipped with a support component. The servo motor (2) and the pendulum (6) are both mounted on the support component. The output shaft of the servo motor (2) is connected to the electromagnet (4) through the drive rod (3). The electromagnet (4) corresponds to the pendulum (6). The vision recognition system is aligned with the pendulum (6). The atomic clock (12) is used to measure the period of a single pendulum.

2. The experimental apparatus for using an atomic clock to measure gravitational acceleration using a simple pendulum according to claim 1, characterized in that: The support components include a servo clamp (1), a support frame (5), and a support rod (15). The support rod (15) is vertically mounted on the base (9). The support frame (5) is mounted on the top of the support rod (15). The servo clamp (1) is mounted on the support frame (5) and is used to fix the servo (2). The pendulum ball (6) is fixed to the support frame (5) by a connecting rope (7).

3. The experimental apparatus for measuring gravitational acceleration using an atomic clock with a simple pendulum according to claim 1, characterized in that: The atomic clock (12) uses a miniaturized traceable rubidium atomic clock module.

4. The experimental apparatus for using an atomic clock to measure gravitational acceleration using a simple pendulum according to claim 1, characterized in that: The visual recognition system includes a camera bracket (14) and a high-definition camera (13) mounted on the camera bracket (14), the high-definition camera (13) being aimed at the pendulum ball (6).

5. The experimental apparatus for using an atomic clock to measure gravitational acceleration using a simple pendulum according to claim 1, characterized in that: A background plate (8) is set behind the electromagnet (4) and the pendulum (6).

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