ࡱ> 5?47 PbjbjUU V7|7|J cl****...BDV<B*! -<)>)>)>)>)>)>)$+ -`b)u.5155b)%**} )%%%5*.<)%5<)%%'V(@J.() loB %) ())0*) '.%'.()%BB**** Caracteristica miscarii Este un caz ideal.Nu exista mediu disipativ, iar energia se conserva.Amplitudinea A= ct Def : Miscarea oscilatorie armonica este miscarea oscilatorie cu amplitudine liniara si constanta in care acceleratia este proportionala cu elongatia si de semn contrar ei. Ecuatiile miscarii oscilatorie armonice Consideram ca punctul material porneste din A.   Ecuatia vitezei v = ve cos  Masa circulara ( =  / t (relatie de definitie) ( = v / R (modul) => v = (R R = A v = (A cos ((t + 0) Conditia de maxim v --> vmax =(t pt.cos (wt + 0) = 1 (t+0 = 2k => t = (2k  0)( Ecuatia acceleratiei acp = (2R sau acp = (2A => a = - (2A sin ((t + 0) Conditia maxima : a ( amax = - (2A pentru sin((t + ) = 1 Asin ((t + 0) = y a = - (2y  Def : Miscarea oscilatorie armonica este o miscare periodica care se repeta identic la intervale egale de timp.Ea este reprezentata printr-o functie periodica. T = 2 / ( In continuare vom studia : Perioada pentru resort elastic Legi : " perioada depinde direct proportional de " m  " perioada depinde invers proportional de " K Observatie : " perioada resortului nu depinde de marimi variabile si nu poate fi influentata. Grupari resorturi : a) Serie   b) Paralel   Perioada pentru pendul matematic   Energia in miscarea oscilatorie armonica Et = Ec + Ep Obs : In miscarea oscilatorie armonica energia se conserva. Et = Epmax ( V = 0 ) Et = Ecmax ( y = 0 ) Scop Et = ? Et = mV2 + Ky2 ; y = A sin (t ; v = (A cos (t Et = m(2A sin2 (t + KA2 sin2 (t ; Et = KA2 (sin2 (t + cos2(t) => Et = KA2 Energia in miscarea oscilatorie armonica pentru resort elastic Ec = mv2 ; Ep = Ky2 ; Et = KA2 Obs. Daca nu se cunoaste viteza si se da in ipoteza valoarea lui A respectiv y se aplica conservarea energiei. Ec = Et Ep ; Ec = KA2 Ky2 ; Ec = K (A2 y2) Energia in miscarea oscilatorie armonica pentru pendul matematic Ec =1/2 mv2 ; H = l l cos  ; H = l (1- cos ) ; Ep = mgh ; Ep = mgl (1- cos ) ( =  / t =>  = (t  = (t R = A sin  = y / A => y = A sin (t Conditia de maxim : y ( ymax = A sin ((t + 0) = +-1 (t +0 = /2 => (t = /2  0 t = (/2  0) / ( Generalizare : t = [(2k+1)/2  0] / (  EMBED Word.Picture.8  Fe = - Ky ; - Ky = ma ; Ky = - m (2 A sin ( t K A sin (t = - m (2 A sin ( t K = (2m ( = " K / m ; 2 / t = " K / m ( = 2 / T ; T = 2 " " m/K y = y1 + y2 ; Constanta echivalenta : 1/Ks = 1/K1 + 1/K2 Ks =K1K2 / (K1 + K2) Ts = 2 " m/Ks Kp =K1 + K2 Tp = 2 "m /Kp Unghiul care corespunde elongatiei :  = elongatie unghiulara  ( y 0 = amplitudine unghiulara 0 (A Gn = G cos  ; Gt = G sin  Gn  la pozitia de extrem este anulata de tensiunea in fir. 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