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Results after Problem 5

The list of the contest leaders after the fifth problem:

Points   Name Country School Physics teacher
12,725   SZABÓ Attila Hungary Leőwey Klára High School, Pécs Simon Péter, Dr Kotek László
11,535   Nikita Sopenko Russia Lyceum No.14, Tambov Valeriy Vladimirovich Biryukov
8,168   Ilie Popanu Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
7,7004   Jakub Šafin Slovak Pavol Horov Secondary, Michalovce Jozef Smrek
7,5883   Lars Dehlwes Germany Ohm-Gymnasium Erlangen Martin Perleth
6,0833   Ivan Tadeu Ferreira Antunes Filho Brazil Colégio Objetivo, Lins, São Paulo  
5,8911   Papimeri Dumitru Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
5,8689   Ion Toloaca Moldova liceul "Mircea Eliade" Igor Iurevici Nemtov; Andrei Simboteanu
5,6695   Brahim Saadi Algeria Preparatory School for Science & Technology of Annaba Derradji Nasreddine
5,5407   Dinis Cheian Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
5,1968   Jakub Supeł  Poland 14th School of Stanisław Staszic, Warsaw Włodzimierz Zielicz
5,0844   Cristian Zanoci Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
4,919   Alexandra Vasileva Russia Lyceum "Second School", Moscow A.R. Zilberman, G.F. Lvovskaya, G.Z. Arabuly 
3,8105   Kohei Kawabata Japan Nada High School  
3,7997   Nadezhda Vartanian Russia Smolensk Pedagogical Lyceum Mishchenko Andrei Anatolievich
3,7517   Luís Gustavo Lapinha Dalla Stella Brazil Colégio Integrado Objetivo, Barueri, Brazil Ronaldo Fogo
3,4205   Bharadwaj Rallabandi India Narayana Jr. College, Basheer Bagh, India Vyom Sekhar Singh
2,5937   Mikhail Shirkin Russia Gymnasium of  Ramenskoye  Petrova Elena Georgyevna
2,1   Krzysztof Markiewicz Poland XIV Highschool in Warsaw Robert Stasiak
2   Jaan Toots Estonia Tallinn Secondary Science School Toomas Reimann
1,903   Petar Tadic Montenegro Gimnazija ,,Stojan Cerovic" Niksic Ana Vujacic
1,8606   Lorenzo Comoglio  Italy Liceo Scientifico del Cossatese e Valle Strona Chiara Bandini
1,6214   Ng Fei Chong Malaysia SMJK Chung Ling, Penang  
1,4641   Hideki Yukawa Japan Nada high school  
1,21   Midhul Varma India Vidyadham Junior, Hyderabad  Manikanta Kumar
1   Teoh Yee Seng Malaysia SMJK HENG EE,Penang; SMJK CHUNG LING,Penang Hong Siang Ean, Loh Pei Yee
1   Task Ohmori Japan Nada High School T.Hamaguchi
1   Sharad Mirani  India Prakash Higher Secondary School Ruchi Sadana, Sunil Sharma
1   Lev Ginzburg Russia Advanced Educational Scientific Center, MSU, Moscow I.V. Lukjanov, S.N. Oks
0,9801   Mekan Toyjanow Turkmenistan Turgut Ozal Turkmen Turkish High School Halit Coshkun
0,81   Meylis Malikov Turkmenistan Turgut Ozal Turkmen Turkish High School Halit Coshkun
0,81   Liara Guinsberg Brazil Colégio Integrado Objetivo, São Paulo, Brazil Ronaldo Fogo
0,792   Ulysse Lojkine  France Lycée Henri IV, Paris M. Lacas
0,72   Rajat Sharma India Pragati Vidya Peeth,Gwalior Mr. Rakesh Ranjan
0,5648   Selver Pepić Bosnia-Herzegovina Fourth Gymnasium Ilidža, Sarajevo Rajfa Musemić


Points for Problem No 5:

3,8876   Nikita Sopenko
2,5678   SZABÓ Attila
2,1436   Ilie Popanu
1,9487   Papimeri Dumitru
1,6105   Cristian Zanoci
1,435   Dinis Cheian
1,2958   Lorenzo Comoglio 
1,0567   Ng Fei Chong
1   Teoh Yee Seng
0,9703   Jakub Šafin
0,81   Ion Toloaca
0,7217   Lars Dehlwes
0,5648   Selver Pepić
0,5134   Petar Tadic


Correct solutions (ordered according to the arrival time; best solutions in bold):

1. Szabó Attila (Hungary)

2. Nikita Sopenko (Russia)

3. Ilie Popanu (Moldova)

4. Papimeri Dumitru (Moldova)

5. Dinis Cheian (Moldova)

6. Cristian Zanoci (Moldova)

7. Ng Fei Chong (Malaysia)

8. Lorenzo Comoglio (Italy)

9. Jakub Šafin (Slovak)

10. Lars Dehlwes (Germany)

11. Petar Tadic (Montenegro)

12. Ion Toloaca (Moldova)

13. Teoh Yee Seng (Malaysia)

14. Selver Pepić (Bosnia-Herzegovina)

(The list is ordered according to the arrival time)

Also, there are two incorrect solutions and two solutions, which are based on correct principles, but contain some mistakes.

Overall number of registered participants: 247 from 42 countries.


Since the number of correct solutions was relatively low, the following hints were given by the end of the third week:

– study the formula sheet (section V-3) to get an idea of how many eigenfrequencies you need to find; if in difficulties counting the number of oscillators, take it equal to the number of degrees of freedom (how many independent loop currents are needed for a superposition to represent arbitrary current distribution of the circuit);

– make use of the strong inequalities at as early stage as possible, to simplify the mathematical task;

– study the section VIII of the formula sheet; particularly useful are pts. 11, 5, 3, 2 (though, depending on your approach, you may not need all of these formulae).

– in order to find the natural frequencies, you can write down the system of differential equations, and based on that system, write down the characteristic equation, the solutions of which are the natural frequencies. However, note that you can avoid writing down the differential equations. Instead, you can make use of the concept of current and voltage resonances. So, for a voltage resonance, there will be a non-zero voltage amplitude U between two nodes A and B, even if there is no current flowing into the node A (and from the node B). Indeed, if the impedance between the nodes A and B is Z=Z(\omega) , we can write |U| = |I||Z|, hence a non-zero U is compatible with I=0 if Z(\omega)=\infty. Therefore, natural frequencies can be found as the solutions of the equation Z(\omega)=\infty.

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