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1 vmarousis.blogspot.com 1 1o 1. ( . ) . 2. , . 1 : 0,2 sec ; : /2 ( ) , . 2: . 40 , ; : 2 , 20 . 3: ( ) 3 ( U ), 80 . ; . ; : H = 3U ( = 2U = U ) 4 , 3. , . : t1 x1=+0,1m t2 x2 = 0,2m x = 0,3m S= 0,5m. 4. , , . : x = t , , = max t, , = max t , F = Fmaxt, . -x +x 0 +0,1 +0,2 -0,1 -0,2 -x http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 2 : : x = +2 + >0, x = 1 1 vmarousis.blogspot.com 3 (1) (2) =0 (1) =0 (2) =1 (1) =1 (2) =2 (1) : sec = max (10t+ ) = max(10 + ) = max( ) >0 sec = max (10t+ ) = max(10 + ) = max( ) 1 vmarousis.blogspot.com 4 9. . : 10. : ) . = - 8(2t + /2). = -max(t+0) : = 2 rad/s , max= 8 2 = 8 = 2m. ) ( 10cm) =10 cm. ) d = 20cm d = 2A = 10cm. ) .. ( ) : : E) x , (...) 11. .... (...) D= m2 : x, , , , . (1) : . ( , . 12. . 1. .., = 3U ; 2. .. ( ) , =3U; : x = At x http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 5 13. . , : 14. , +x x , , , ( ). . (1) (2) : 1 = 2 , U1 = U2 , F1 = F2 , 1 = 2 , 1 = 2 . -x= - d/2 +x = + d/2 .. 1 F1 1 F2 2 2 1 2 - + d http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 6 15. . . . ( k ) , 1/m. Hooke : F= k ( ) . F . F = 0 w = F : F = w F F= D x, x . . ( ) .. . : = : = , .... = ( ). (. 3 ) (. 4) w x= k F = F w F F x (. 1) (. 2) http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 7 16. .. D . 1 : .. F = 0 . 2 : x , (F) , . 3 : F, : F = Dx D . 4 : D . : ) (. 2) : F = F = k x ( 1). .. F = D x ( 2) . ( 1) ( 2) D = k B) : (. 3) F = 0 w = F w = k (3) ( . 4) : F = w F F = w k( F = w k F = k x (4) .. F = D x (2) . (4) (2) D = k http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 8 17. 18. : 4, . , . , . , . ( ), ( ), ( ). = U, , U 0, . ( ) ( ) . < 0 > 0 -A +A 0 + - = - = 0 = +max F = +Fmax K = 0 U = Umax = + = 0 = -max F = -Fmax K = 0 U = Umax = 0 = max = 0 F = 0 K = Kmax U = 0 > 0, F>0 < 0, F< 0 http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 9 19. . a. . b. . c. , i) , F = 0. ii) , =0. iii) , x 0. d. : e. , x . f. x = (t+0) , = (t+0), = 2(t+0) 20. ...; , : F = m, F = m2x : m = 3 kg = 0,4m k = 150 N/m. . : F=w kx0 = mg, x0= mg/k = 0,2m x, w F. Newton : F + w = m F+w = m2x F = m2x w D = k = m2, : F = kx , : F = 150x 30 (S.I.). x. x0 x W W F0 F http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 10 21. .. = 1= 2. D1 = m1 2 D2 = m2 2, D = (m1+ m2) 2. D = D1+D2 22. . : A1= 2A2 T1 = 2T2 2 = 21 : = : : : 23. ( ) ( ..). m1 m2 A1 A2 t x http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 11 .. . : .. : .. : 2 1 m2 m1 (+) m1 m2 m1 m2 1 2 1 2 (+) m1 m2 1 2 (+) http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 12 .. . . H .. : .. . m1 . ( ) ( ) ( ) ( V ) .. . . . . . ( . ) : F= 0 g = k . : F = 0 (+m)g = k(+x) . 2 1 .. & . (+) m x http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 13 24. ( ) m1 ... m2 , , : ) , . ) m1. ) ... : F = -D1x F = - m12 x (1) , , (1) : F = m12 x m1g = m12 x x = (2) : max = m1(g + 2) . x = + (2) : min = m1(g 2) (3) . () , : min 0 (3), m1(g 2) 0 g 2 , , f . 25. ) : . ) : F . ) : ) : N = m1(g 2x) (2) N m1 m2 m1gg x + http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 14 1. . , . 2. ( ) . . 3. . ) t= 0 (1) . Vmax= E , Q . (2) q= Q i = 0 . q = Q(t) I = I(t) . = Q ) L C E,r L (1) (2) Q -------- ++++++ (2) ----- C ++++ Q E,r L (1) i i E,r E,r L L C C i i i i _ _ _ + + + http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 15 . . . . . () : t = 0 ,I = +I, q = 0 I = -I (t+) I = -I = -1 = = rad : ) t=0 , : : t=0 . t = 0 . , . LC , .. . 4. q,i,Q,I, ... . (1) : 5. q UE UB. UE= 3UB (1) Q . .. : http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 16 (2) (2) q= Q (t) (2) : : , : , : : , , . 6. . 7. ) : ) : ) : UE + UB = . (1) ) : VL = VC 8. : (i) . : i http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 17 , . , , , . : (1) . (1) t = T t = (N+1)T = 0, 1, 2, : : () . 1. F = - b, . +1 +1. : , . (-) (+) C L i (-) (+) i L C http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 18 . : 20%. 4 10cm 5 ; : 20% 80% 5= 0,8 4 = 0,8 10 = 8cm. 2. F= -b k . : 0= 40cm = 2sec-1. = 10cm; : t= t = 3. F = -b 1 t1 2 t2 . : t = 0 = 25cm. t1= 20sec 1= 16cm, 2 t2= 30sec ; : = = = 25 : 4. : 5. http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 19 ( : F) . : 1. H . , 2. , . . . . 3. . x = (t + ) , = max (t+0) , = - max(t+0) , F= - b = - b (t+) : = =2f , f . : : = = 2f , f . A o1 A o f o f 1 f 2 A o2 f http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 20 . : 4. , F= F F= b. . : F= F , x = 0. 5. =. > max>Umax . http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 21 1. .. x1= A1(t) x2= A2(t+) : x = A(t+) . 2. , , : 1 2 x1 x2 x = x1+x2 1 2 = 1+2 1 2 = 1+2 1 2 1 2 1 2 01 02 3. D D = m2 . , A A2 A1 x2 x x1 t http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 22 , , . . . 1 2 . , : (1) (2) (3) (1) (2) (3): , . = /2 = 90 http://vmarousis.blogspot.com/ 1 vmarousis.blogspot.com 23 4. .. 1 : x1= 1t 2 : x2 = 2t : x = x1+x2 = 1t + 2t = . . . . . .. , . 1 2 (1) . : : : H : 5. O : 6. , . http://vmarousis.blogspot.com/