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Open Access Journal of
eISSN: 2641-9335

Mathematical and Theoretical Physics

Opinion Volume 1 Issue 4

Resonance and the superforce

Paul TE Cusack

Park Ave, Saint John, Canada

Correspondence: Paul TE Cusack, BScE, Dule 23 Park Ave,Saint John, NB E2J 1R2, Canada, Tel 5066 5263 50

Received: June 22, 2018 | Published: August 9, 2018

Citation: Paul TEC. Resonance and the superforce. Open Acc J Math Theor Phy. 2018;1(4):152-153. DOI: 10.15406/oajmtp.2018.01.00025

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Abstract

In this brief paper, we provide some calculations from Wave mechanics, namely Resonance. We see that the universe is stoked by the superforce, and that energy is dampened by the mass. When taken with gravity, the characteristic equation for the universe results.

Keywords: superforce, astrotheology, resonance, golden mean equation

Introduction

Using variables calculated in this author’s previous papers, we derive the characteristic equation for the universe working with the formulas that are used to determine resonance conditions.1,2

tan δ=[ 1/Q ]/[ ( ω 0 /ω ) ( ω/ ω 0 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWG0bGaamyyaiaad6gacaqGGaGaeqiTdqMaeyypa0Zdamaa dmaabaWdbiaaigdacaGGVaGaamyuaaWdaiaawUfacaGLDbaapeGaai 4la8aadaWadaqaamaabmaabaWdbiabeM8a3naaBaaajuaibaGaaGim aaqcfayabaGaai4laiabeM8a3bWdaiaawIcacaGLPaaapeGaaeiiai abgkHiT8aadaqadaqaa8qacqaHjpWDcaGGVaGaeqyYdC3damaaBaaa juaibaWdbiaaicdaaKqba+aabeaaaiaawIcacaGLPaaaaiaawUfaca GLDbaaaaa@5609@

δ=π/4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaH0oazcqGH9aqpcqaHapaCcaGGVaGaaGinaaaa@3DB4@  (phase angle)

Q=1/2

Therefore ω= ω 0 =1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDcqGH9aqpcqaHjpWDdaWgaaqcfasaaiaaicdaaKqb agqaaiabg2da9iaaigdaaaa@3FD3@

A= F 0 /k  { [ ω ω 0 ]/ [ ( ω 0 /ω )( ω/ ω 0 ) ] 2 +( 1/ Q 2 )] } 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGbbGaeyypa0JaamOra8aadaWgaaqcfasaa8qacaaIWaaa juaGpaqabaWdbiaac+cacaWGRbGaaeiia8aadaGadaqaamaadmaaba WdbiabeM8a3jabeM8a39aadaWgaaqcfasaa8qacaaIWaaajuaGpaqa baaacaGLBbGaayzxaaWdbiaac+capaWaamWaaeaadaqadaqaa8qacq aHjpWDpaWaaSbaaKqbGeaapeGaaGimaaqcfa4daeqaa8qacaGGVaGa eqyYdChapaGaayjkaiaawMcaa8qacqGHsislpaWaaeWaaeaapeGaeq yYdCNaai4laiabeM8a39aadaWgaaqcfasaa8qacaaIWaaapaqabaaa juaGcaGLOaGaayzkaaaacaGLBbGaayzxaaWaaWbaaKqbGeqabaGaaG OmaaaajuaGpeGaey4kaSYdamaabmaabaWdbiaaigdacaGGVaGaamyu amaaCaaajuaibeqaaiaaikdaaaaajuaGpaGaayjkaiaawMcaaiaac2 faaiaawUhacaGL9baadaahaaqcfasabeaapeGaaGymaiaac+cacaaI Yaaaaaaa@66FF@

F=8/3

k=0.4233

ω= ω 0 =1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDcqGH9aqpcqaHjpWDdaWgaaqcfasaaiaaicdaaKqb agqaaiabg2da9iaaigdaaaa@3FD3@

Q=1/2

Therefore A=125.99126= E min MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGbbGaeyypa0JaaGymaiaaikdacaaI1aGaaiOlaiaaiMda caaI5aGaeSipIOJaaGymaiaaikdacaaI2aGaeyypa0Jaamyra8aada Wgaaqcfasaa8qacaWGTbGaamyAaiaad6gaa8aabeaaaaa@4695@

E min 1587=1sin 1=Moment. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGfbWdamaaBaaajuaibaWdbiaad2gacaWGPbGaamOBaaWd aeqaaKqba+qacaaIXaGaaGynaiaaiIdacaaI3aGaeyypa0JaaGymai abgkHiTiaadohacaWGPbGaamOBaiaabccacaaIXaGaeyypa0Jaamyt aiaad+gacaWGTbGaamyzaiaad6gacaWG0bGaaiOlaaaa@4DBB@

1-0.1587=8425

1/0.8425=118.87 = Mass Periodic Table of the elements.

ω m =( 1 ) ( 11/  [ 2 ( 1/2 ) ) 2 ] 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDpaWaaSbaaKqbGeaapeGaamyBaaWdaeqaaKqba+qa cqGH9aqppaWaaeWaaeaapeGaaGymaaWdaiaawIcacaGLPaaadaqcWa qaa8qacaaIXaGaeyOeI0IaaGymaiaac+cacaqGGaWdamaajibabaWd biaaikdacaqGGaWdamaabmaabaWdbiaaigdacaGGVaGaaGOmaaWdai aawIcacaGLPaaaaiaawUfacaGLPaaadaahaaqcfasabeaacaaIYaaa aaqcfaOaayjkaiaaw2faamaaCaaajuaibeqaaiaaigdacaGGVaGaaG Omaaaaaaa@502E@

= (1) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqGH9aqpdaGcaaqaaiaacIcacqGHsislcaaIXaGaaiykaaqa baaaaa@3BF2@

=-0.618

ω 0 < ω m   MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDpaWaaSbaaKqbGeaapeGaaGimaaqcfa4daeqaa8qa cqGH8aapcqaHjpWDpaWaaSbaaKqbGeaapeGaamyBaaWdaeqaaKqba+ qacaGGGcaaaa@417F@  

Therefore, α=π MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHXoqycqGH9aqpcqaHapaCaaa@3C3D@

A m = A 0 =1/2 /[ 14 ( 1/2 ) 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGbbWdamaaBaaajuaibaWdbiaad2gaa8aabeaajuaGpeGa eyypa0Jaamyqa8aadaWgaaqcfasaa8qacaaIWaaapaqabaqcfa4dbi abg2da9iaaigdacaGGVaGaaGOmaiaabccacaGGVaWdamaadmaabaWd biaaigdacqGHsislcaaI0aWdamaabmaabaWdbiaaigdacaGGVaGaaG OmaaWdaiaawIcacaGLPaaadaahaaqcfasabeaacaaIYaaaaaqcfaOa ay5waiaaw2faaaaa@4CC7@

= A 0 1/0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqGH9aqpcaWGbbWdamaaBaaajuaibaWdbiaaicdaaKqba+aa beaapeGaaGymaiaac+cacaaIWaaaaa@3DA4@

= MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqGH9aqpcqGHEisPaaa@3A52@

ω m = ω 0 {11/( 2 Q 2 )] 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDpaWaaSbaaKqbGeaapeGaamyBaaqcfa4daeqaa8qa cqGH9aqpcqaHjpWDpaWaaSbaaKqbGeaapeGaaGimaaWdaeqaaKqbak aacUhapeGaaGymaiabgkHiTiaaigdacaGGVaWdamaabmaabaWdbiaa ikdacaWGrbWaaWbaaKqbGeqabaGaaGOmaaaaaKqba+aacaGLOaGaay zkaaGaaiyxamaaCaaajuaibeqaaiaaigdacaGGVaGaaGOmaaaaaaa@4CB0@

ω m /  ω 0 =0.935 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVye9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDpaWaaSbaaKqbGeaapeGaamyBaaWdaeqaaKqba+qa caGGVaGaaeiiaiabeM8a39aadaWgaaqcfasaa8qacaaIWaaajuaGpa qabaWdbiabg2da9iaaicdacaGGUaGaaGyoaiaaiodacaaI1aaaaa@455B@

=mp+

A m = A 0 [ Q ]/ [ 11/4 Q 2 ] 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVye9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGbbWdamaaBaaajuaibaWdbiaad2gaaKqba+aabeaapeGa eyypa0Jaamyqa8aadaWgaaqcfasaa8qacaaIWaaajuaGpaqabaWaam WaaeaapeGaamyuaaWdaiaawUfacaGLDbaapeGaai4la8aadaWadaqa a8qacaaIXaGaeyOeI0IaaGymaiaac+cacaaI0aGaamyuamaaCaaaju aibeqaaiaaikdaaaaajuaGpaGaay5waiaaw2faamaaCaaabeqcfasa aiaaigdacaGGVaGaaGOmaaaaaaa@4CC4@

A m / A 0 =2.06 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGbbWdamaaBaaajuaibaWdbiaad2gaaKqba+aabeaapeGa ai4laiaadgeapaWaaSbaaKqbGeaapeGaaGimaaqcfa4daeqaa8qacq GH9aqpcaaIYaGaaiOlaiaaicdacaaI2aaaaa@41EA@

=γ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqGH9aqpcqaHZoWzaaa@3A88@

=dM/dt

ω/ ω 0 = ( 11/2 Q 2 ) 1/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDcaGGVaGaeqyYdC3damaaBaaajuaibaWdbiaaicda aKqba+aabeaapeGaeyypa0ZdamaabmaabaWdbiaaigdacqGHsislca aIXaGaai4laiaaikdacaWGrbWaaWbaaKqbGeqabaGaaGOmaaaaaKqb a+aacaGLOaGaayzkaaWaaWbaaKqbGeqabaGaaGymaiaac+cacaaIYa aaaaaa@4976@

=0.935

=11/2 Q 2 = ( 0.938.7 ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqGH9aqpcaaIXaGaeyOeI0IaaGymaiaac+cacaaIYaGaamyu amaaCaaajuaibeqaaiaaikdaaaqcfaOaeyypa0ZdamaabmaabaWdbi aaicdacaGGUaGaaGyoaiaaiodacaaI4aGaaiOlaiaaiEdaa8aacaGL OaGaayzkaaWaaWbaaeqajuaibaGaaGOmaaaaaaa@480D@

11/2 Q 2 =88.12 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaaIXaGaeyOeI0IaaGymaiaac+cacaaIYaGaamyuamaaCaaa juaibeqaaiaaikdaaaqcfaOaeyypa0JaaGioaiaaiIdacaGGUaGaaG ymaiaaikdaaaa@42D0@

1/2 Q 2 =118.72 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaaIXaGaai4laiaaikdacaWGrbWaaWbaaKqbGeqabaGaaGOm aaaajuaGcqGH9aqpcaaIXaGaaGymaiaaiIdacaGGUaGaaG4naiaaik daaaa@41E2@

1/ Q 2 =23.65 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaaIXaGaai4laiaadgfadaahaaqcfasabeaacaaIYaaaaKqb akabg2da9iaaikdacaaIZaGaaiOlaiaaiAdacaaI1aaaaa@4069@

Q=0/.1537=1/6.5=1/G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGrbGaeyypa0JaaGimaiaac+cacaGGUaGaaGymaiaaiwda caaIZaGaaG4naiabg2da9iaaigdacaGGVaGaaGOnaiaac6cacaaI1a Gaeyypa0JaaGymaiaac+cacaWGhbaaaa@46B3@

Q=0.1537=1/6.50~1/ G 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGrbGaeyypa0JaaGimaiaac6cacaaIXaGaaGynaiaaioda caaI3aGaeyypa0JaaGymaiaac+cacaaI2aGaaiOlaiaaiwdacaaIWa GaaiOFaiaaigdacaGGVaGaam4ramaaBaaajuaibaGaaGimaaqcfaya baaaaa@484D@

ω m / ω 0 =( 11/2  G 2 )=Mp+ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDpaWaaSbaaKqbGeaapeGaamyBaaqcfa4daeqaa8qa caGGVaGaeqyYdC3damaaBaaajuaibaWdbiaaicdaa8aabeaajuaGpe Gaeyypa0ZdamaabmaabaWdbiaaigdacqGHsislcaaIXaGaai4laiaa ikdacaqGGaGaae4ramaaCaaajuaibeqaaiaaikdaaaaajuaGpaGaay jkaiaawMcaa8qacqGH9aqpcaWGnbGaamiCaiabgUcaRaaa@4D5F@

G 0 /| Det. | = 3 MP+ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWaaSbaaKqbGeaacaaIWaaajuaGbeaacaGGVaWdamaa emaabaWdbiaadseacaWGLbGaamiDaiaac6caa8aacaGLhWUaayjcSd WdbiaabccacqGH9aqpdaGcaaqaaiaaiodaaeqaamaakaaabaGaamyt aiaadcfacqGHRaWkaeqaaaaa@46BE@

G 0 /Mp+=| D | 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWaaSbaaKqbafaacaaIWaaajuaGbeaacaGGVaGaamyt aiaadchacqGHRaWkcqGH9aqppaWaaqWaaeaapeGaamiraaWdaiaawE a7caGLiWoacaaMc8+aaOaaaeaacaaIZaaabeaaaaa@4531@

| D |=4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfa4aaqWaae aaqaaaaaaaaaWdbiaadseaa8aacaGLhWUaayjcSdWdbiabg2da9iaa isdaaaa@3DA9@

G 0 /Mp+=6928( 938 )=6.50 G 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWaaSbaaKqbGeaacaaIWaaajuaGbeaacaGGVaGaamyt aiaadchacqGHRaWkcqGH9aqpcaaI2aGaaGyoaiaaikdacaaI4aWdam aabmaabaWdbiaaiMdacaaIZaGaaGioaaWdaiaawIcacaGLPaaapeGa eyypa0JaaGOnaiaac6cacaaI1aGaaGimaiablYJi6iaadEeadaWgaa qcfasaaiaaicdaaeqaaaaa@4C99@

1/6.928=1443=1Ln π MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaaIXaGaai4laiaaiAdacaGGUaGaaGyoaiaaikdacaaI4aGa eyypa0JaaGymaiaaisdacaaI0aGaaG4maiabg2da9iaaigdacqGHsi slcaWGmbGaamOBaiaabccacqaHapaCaaa@47C8@

G 0 ={1/( 1Ln π )] Mp+ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWaaSbaaKqbGeaacaaIWaaajuaGbeaacqGH9aqppaGa ai4Ea8qacaaIXaGaai4la8aadaqadaqaa8qacaaIXaGaeyOeI0Iaam itaiaad6gacaqGGaGaeqiWdahapaGaayjkaiaawMcaaiaac2fapeGa aeiiaiaad2eacaWGWbGaey4kaScaaa@4990@

1/( 1Ln π )=1/t=E MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaaIXaGaai4la8aadaqadaqaa8qacaaIXaGaeyOeI0Iaamit aiaad6gacaqGGaGaeqiWdahapaGaayjkaiaawMcaa8qacqGH9aqpca aIXaGaai4laiabgkHiTiaadshacqGH9aqpcqGHsislcaWGfbaaaa@47F3@

G 0 =1/t ( 11/2 G 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWdamaaBaaajuaibaWdbiaaicdaaKqba+aabeaapeGa eyypa0JaaGymaiaac+cacaWG0bGaaeiia8aadaqadaqaa8qacaaIXa GaeyOeI0IaaGymaiaac+cacaaIYaGaam4ra8aadaahaaqcfasabeaa peGaaGOmaaaaaKqba+aacaGLOaGaayzkaaaaaa@469A@

G 0 =E( 11/2 G 0 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWdamaaBaaajuaibaWdbiaaicdaaKqba+aabeaapeGa eyypa0Jaamyra8aadaqadaqaa8qacaaIXaGaeyOeI0IaaGymaiaac+ cacaaIYaGaam4ramaaDaaajuaibaGaaGimaaqaaiaaikdaaaaajuaG paGaayjkaiaawMcaaaaa@44F5@

G 0 =E( 11/2  G 0 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWdamaaBaaajuaibaWdbiaaicdaaKqba+aabeaapeGa eyypa0Jaamyra8aadaqadaqaa8qacqGHsislcaaIXaGaeyOeI0IaaG ymaiaac+cacaaIYaGaaeiiaiaadEeadaqhaaqcfasaaiaaicdaaeaa caaIYaaaaaqcfa4daiaawIcacaGLPaaaaaa@4685@

G 0 t=( 11/2  G 0 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWdamaaBaaajuaibaWdbiaaicdaaKqba+aabeaapeGa amiDaiabg2da98aadaqadaqaa8qacqGHsislcaaIXaGaeyOeI0IaaG ymaiaac+cacaaIYaGaaeiiaiaadEeadaqhaaqcfasaaiaaicdaaeaa caaIYaaaaaqcfa4daiaawIcacaGLPaaaaaa@46B4@

(( 1/2 ) G 0 2 )1Gt=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaOaaiikam aabmaabaaeaaaaaaaaa8qacaaIXaGaai4laiaaikdaa8aacaGLOaGa ayzkaaWdbiaadEeadaqhaaqcfasaaiaaicdaaeaacaaIYaaaaKqba+ aacaGGPaWdbiabgkHiTiaaigdacqGHsislcaWGhbGaamiDaiabg2da 9iaaicdaaaa@465F@

G 0 2 2Gt1=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWaa0baaKqbGeaacaaIWaaabaGaaGOmaaaajuaGcqGH sislcaaIYaGaam4raiaadshacqGHsislcaaIXaGaeyypa0JaaGimaa aa@41D1@

For t=1/2   E min MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWG0bGaeyypa0JaaGymaiaac+cacaaIYaGaaeiiaiabgkzi UkaabccacaWGfbWdamaaBaaajuaibaWdbiaad2gacaWGPbGaamOBaa qcfa4daeqaaaaa@43DF@

G 0 2 G1=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbWaa0baaKqbGeaacaaIWaaabaGaaGOmaaaajuaGcqGH sislcaWGhbGaeyOeI0IaaGymaiabg2da9iaaicdaaaa@401C@

Golden Mean Parabola

F=Ma=-ks

s=A(sin ( ωt+φ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGZbGaeyypa0Jaamyqa8aacaGGOaWdbiaadohacaWGPbGa amOBaiaabccapaWaaeWaaeaapeGaeqyYdCNaamiDaiabgUcaRiabeA 8aQbWdaiaawIcacaGLPaaaaaa@4602@

Let A=1; ω=1; t=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGbbGaeyypa0JaaGymaiaacUdacaqGGaGaeqyYdCNaeyyp a0JaaGymaiaacUdacaqGGaGaamiDaiabg2da9iaaigdaaaa@436E@

s=sin θ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGZbGaeyypa0Jaam4CaiaadMgacaWGUbGaaeiiaiabeI7a Xbaa@3F0B@

But s=E×t=| E || t |sinθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGZbGaeyypa0JaamyraiabgEna0kaadshacqGH9aqppaWa aqWaaeaapeGaamyraaWdaiaawEa7caGLiWoadaabdaqaa8qacaWG0b aapaGaay5bSlaawIa7a8qacaWGZbGaamyAaiaad6gacaaMc8UaeqiU dehaaa@4D37@

E=1=t

s=sinθ Ma=ks MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGZbGaeyypa0Jaam4CaiaadMgacaWGUbGaaGPaVlabeI7a XjaabccacaWGnbGaamyyaiabg2da9iabgkHiTiaadUgacaWGZbaaaa@4629@

117.33 ( 1/ 2 ) =0.4233 sinθ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaaIXaGaaGymaiaaiEdacaGGUaGaaG4maiaaiodacaqGGaWd amaabmaabaWdbiaaigdacaGGVaWaaOaaaeaacaaIYaaabeaaa8aaca GLOaGaayzkaaWdbiaabccacqGH9aqpcqGHsislcaaIWaGaaiOlaiaa isdacaaIYaGaaG4maiaaiodacaqGGaGaam4CaiaadMgacaWGUbGaaG PaVlabeI7aXbaa@4E95@

sinθ=196= MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGZbGaamyAaiaad6gacaaMc8UaeqiUdeNaeyypa0JaaGym aiaaiMdacaaI2aGaeyypa0JaeyOhIukaaa@43B0@

sin 0.196=88.47= ε 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGZbGaamyAaiaad6gacaqGGaGaaGimaiaac6cacaaIXaGa aGyoaiaaiAdacqGH9aqpcaaI4aGaaGioaiaac6cacaaI0aGaaG4nai abg2da9iabew7aLnaaBaaajuaibaGaaGimaaqcfayabaaaaa@4800@  Permitivity

Figure 1

Figure 1 Gravity and anti-gravity in balance.

Clairnaut

E-G=0

where 

G= d 2 E/d t 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGhbGaeyypa0JaamizamaaCaaajuaibeqaaiaaikdaaaqc faOaamyraiaac+cacaWGKbGaamiDamaaCaaajuaibeqaaiaaikdaaa aaaa@409B@

Ma=MG=118(6,52)=0.769

θ=ωt+φ=0.196 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaH4oqCcqGH9aqpcqaHjpWDcaWG0bGaey4kaSIaeqOXdOMa eyypa0JaaGimaiaac6cacaaIXaGaaGyoaiaaiAdaaaa@44AC@

=0.196+π/4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqGH9aqpcaaIWaGaaiOlaiaaigdacaaI5aGaaGOnaiabgUca Riabec8aWjaac+cacaaI0aaaaa@409B@

=0.5839

t=1

ω= 0.5939 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDcqGH9aqpdaGcaaqaaiaaicdacaGGUaGaaGynaiaa iMdacaaIZaGaaGyoaaqabaaaaa@3F2C@

=0.7677

ω= ( k/M ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHjpWDcqGH9aqpdaGcaaqaa8aadaqadaqaa8qacaWGRbGa ai4laiaad2eaa8aacaGLOaGaayzkaaaapeqabaaaaa@3EFA@

α=( N1 )δ/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHXoqycqGH9aqppaWaaeWaaeaapeGaamOtaiabgkHiTiaa igdaa8aacaGLOaGaayzkaaWdbiabes7aKjaac+cacaaIYaaaaa@41D6@

α=π=( N1 ) π/4/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaHXoqycqGH9aqpcqaHapaCcqGH9aqppaWaaeWaaeaapeGa amOtaiabgkHiTiaaigdaa8aacaGLOaGaayzkaaWdbiaabccacqaHap aCcaGGVaGaaGinaiaac+cacaaIYaaaaa@46C5@

N=9= c 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGobGaeyypa0JaaGyoaiabg2da9iaadogadaahaaqcfasa beaacaaIYaaaaaaa@3D71@

So we have:

E; t;s;M; ε 0 ; G 0 ;k;ω MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacaWGfbGaai4oaiaabccacaWG0bGaai4oaiaadohacaGG7aGa amytaiaacUdacqaH1oqzpaWaaSbaaKqbGeaapeGaaGimaaqcfa4dae qaa8qacaGG7aGaam4ra8aadaWgaaqcfasaa8qacaaIWaaapaqabaqc fa4dbiaacUdacaWGRbGaai4oaiabeM8a3baa@4A1E@

δ( v=a ); θ and  c 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVKe9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqcfaieaaaaaa aaa8qacqaH0oazpaWaaeWaaeaapeGaamODaiabg2da9iaadggaa8aa caGLOaGaayzkaaWdbiaacUdacaqGGaGaeqiUdeNaaeiiaiaadggaca WGUbGaamizaiaabccacaWGJbWaaWbaaKqbGeqabaGaaGOmaaaaaaa@4742@

Conclusion

We see that the Surperforce acts on the exterior universe producing resonance effects.3,4 The characteristic equation results, as well as mass of the proton and the periodic table of the elements mass.

Acknowledgements

None.

Conflict of interest

The author declares that there is no conflict of interest.

References

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