1 / 26

Designing an Electronic System for the Study of Simple Pendulum at Large Angles

Designing an Electronic System for the Study of Simple Pendulum at Large Angles. Presented by: Abdulghefar Kamil Faiq Assistant Lecturer Physics Department. This article has been published at the Journal of Asian Scientific Researches JASR Vol. 2 No. (5) pp. 281-291 at the following links:.

lovie
Download Presentation

Designing an Electronic System for the Study of Simple Pendulum at Large Angles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Designing an Electronic System for the Study of Simple Pendulum at Large Angles • Presented by: • Abdulghefar Kamil Faiq • Assistant Lecturer • Physics Department

  2. This article has been published at the Journal of Asian Scientific Researches JASR Vol. 2 No. (5) pp. 281-291 at the following links: http://ideas.repec.org/s/asi/joasrj.html http://socionet.ru/publication.xml?h=repec:asi:joasrj:2012:p:281-291 http://www.aessweb.com/archives.php?m=May2012&id=5003 http://www.atifali.com/abstract/JASR/1319.htm Goto slid 11

  3. Introduction One of the first topics that physics students learn is the acceleration of bodies falling toward the center of the earth. The magnitude g of the acceleration due to gravity is usually determined in undergraduate laboratories by measuring the period of a simple pendulum Yet students sometimes fail to appreciate why the initial angular displacement of the pendulum must be small?

  4. . A simple pendulum is an idealization of a real pendulum. It consists of an infinitely light rigid rod attached to a frictionless pivot point, and a point mass attached to the free end of rigid rod. The motion of the simple pendulum is described by an angle displacement of the pendulum from its vertical equilibrium position. For small amplitude of the angle, the motion of a simple pendulum is well described by a linear simple harmonics. For the large angle, on the other hand, the motion of the simple pendulum is described by a nonlinear differential equation

  5. The aim of the Study • In this work, we designed a simple electronic circuit, feeds a sophisticated CRO, to measure the instantaneous time period of pendulum's oscillatory motion at high level of accuracy. This work aims at the study of the amplitude of vibration's effect on the time period, damping of the pendulum, and the technical factors that affect the measuring system. All these are to further investigate the pendulum's problem at large displacement angles.

  6. Theoretical Basis The analysis of simple pendulum is important in numerous areas of mathematics and physics, it is an important example of non-linear differential equation and does not have an analytic solution except for the special case where the angular displacement is small when it can be linearized and the problem reduces to a harmonic oscillator. The equation of motion is given as follows: (eq 1) Where The above equation is a non linear differential equation it has no analytic solution except for the case of small angles :

  7. as (in radian), and eq. (1) becomes: • (eq 2) This is the differential equation of simple harmonic motion of angular frequency of o. The solution of eq. (2) gives time period (To) of (eq 3) Taking into account the large displacement angles (when the above approximation cannot be used), the solution of eq. (1) will be • (eq 4) • second order approximation of Bernoulli can be used : • (eq 5)

  8. We can use the following equation for calculation of the damped amplitude angles with period number: • (eq 6) • Displacement angle damping follows the following equation : • (eq 7) • Where m is the initial displacement angle,  is the damping factor, we assume that the instantaneous time period t is slightly changed with number of period n, then we can define  as another damping parameter that deals with n. Substituting equation (eq 7) into equation (5) gives : • (eq 8)

  9. Theoretical g in Erbil • The theoretical value of g in Erbil city at College of science (414 m, Latitude 36o 09' 10'') can be calculated by using the following equation (Li, and Gotze, 2001): • (9) • Where: gQ= acceleration in cm/sec2, lamda is the latitude, and h is the high above sea level in meter The above equation is called the international gravity formula (1980) with first correction for high above sea level; the result is 979.705 cm/sec2.

  10. Method • The following electronic system is designed: • a- Protractor • b- Stand • c- Photo gate • d- The designed electronic switch circuit • e- A thread and a bob

  11. The following is the designed electronic circuit

  12. Some Photos

  13. The output signal snapshot on the CRO screen practical

  14. Measurement of the output signal ‘s parameters

  15. Results Graph (1): Displays the squared time period T2 as a function of the pendulum's length L, for five initial amplitudes 5o, 10o, 15o, 20o, and 25o.

  16. Graph(2): g' as a function of pendulum length for five initial amplitudes 5o, 10o, 15o, 20o, and 25o.

  17. o in degrees 5 10 15 20 25 • g in cm/sec2 980.5866 977.9147 974.5351 969.9856 965.2425 • g' in cm/sec2 981.520 981.6419 982.9022 984.8156 988.3503 • R2 0.9998 0.9999 0.9999 0.9999 0.9999 • Table(1): g and g' as calculated from the slopes of Graph(1) • Calculated g in erbil by using equation(9) is: • 979.705 cm/sec2 • L in cm 60 70 80 95 Figure(5) • g in cm/sec2 984.0273 984.0115 981.1396 978.931 980.5866 • g' in cm/sec2 984.9642 984.9485 982.0739 979.863 981.520 • Table (2): g and g' for different pendulum's lengths for the case of constant o of 5 o

  18. Graph(3): Time period To change with period number (n) for five initial amplitudes 5o, 10o, 15o, 20o, and 25o

  19. Graph(4): The displacement angle as a function of period number (n) for five initial amplitudes 5o, 10o, 15o, 20o, and 25o.

  20. o 5o 10o 15o 20o 25o •  0.004235 0.00353 0.004808 0.005537 0.00621 • R2 0.9896 0.9682 0.9909 0.9753 0.9631 • Table (3): Results of curve fitting of Graph(4)

  21. Graph(5): The maximum velocity Vm as a function of period's number (n) for five initial amplitudes 5o, 10o, 15o, 20o, and 25o.

  22. Graph(6): Calculated g' as a function of period number for o=5o compared with calculated g' averaged for 80 periods, and the corrected g'.

  23. Conclusion • The problem of simple pendulum at large angles can be studied by the above presented technique. • The results of the local g' at Erbil city for o=5o, L=95 cm and the average time is taken for 80 periods gives a relative error of 0.003256%. • The instantaneous measurements of To, Vmax, and o can be performed with this system, the results are comparable with the theory. • Error sources of the instantaneous To measurements can be related to the operating time of the three used relays, its found out that by adding the maximum operating time of these relays to the instantaneous time period To for o=5o , results of g' approaches that of the g' averaged for 80 periods.

  24. This article has been published at the Journal of Asian Scientific Researches JASR Vol. 2 No. (5) pp. 281-291 at the following links: http://ideas.repec.org/s/asi/joasrj.html http://socionet.ru/publication.xml?h=repec:asi:joasrj:2012:p:281-291 http://www.aessweb.com/archives.php?m=May2012&id=5003 http://www.atifali.com/abstract/JASR/1319.htm

  25. Thanks for your attendance

More Related