,
m - , r - .
- .
:
,
- , , a - , m - .
, l - , .
, R - , .
, R - .
, R - , .
- .
M - , .
F - , h - - .
J=const
- .
:
,
- i - , .
1. , a , 1) , 2) . . .
:
1) ; 2) , .
, .
II OX.
. (1)
, (2)
- , - .
, R, .
.
(2):
.
(3) (1):
. (4)
,
,
: ,
2. , . . .
C- . . , : .
J - , , w - .
. (1)
.
:
.
(1),
.
: .
3. , . . , . .
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. .
(1)
, - .
(2)
. (3)
(2) mVl - . , r = l,
(2) (3):
; (4)
. (5)
(5) (4), :
. (6)
(6) (4),
. (7)
(2), (7)
:
4.1. , m = 500 , , m1 = 100 m2 = 120 . , ? .
4.2. m = 100 R = 5 ν = 8 -1. F = 40 , τ = 10 . .
4.3. t l = 2 h = 10 ?
4.4. m = 10 R = 20 , . φ = + Bt2 + t3, = 4 /2, = - 1 /3. , . τ = 2 .
4.5. l = 50 m = 40 ε = 3 /2 , : 1) , 2) . .
4.6. m1 = 0,25 m2 = 0,15 , . , m1. ? m1 μ = 0,3. m0 = 0,1 , . .
4.7. m = 0,2 , m1 = 0,3 m2 = 0,5 . 1 2 , .
4.8. m = 100 R = 40 n = 480 /. , τ = 80 .
4.9. R = 10 , m = 2 . , V = 2 8 t (/). . .
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4.10. m0 = 5 R = 20 . , m1 = 3 . , m1 .
4.11. m0 = 3 , R = 10 , m1 = 2 m2 = 1 . . .
4.12. , J = 69,6 ×2, ω = 31,4 /. , τ = 20 .
4.13. , . m2 = 5 , V = 5 + 0,8 t (/), m1 . J= 5×10-2 ×2, R = 0,2 . m1. .
4.14. R = 40 , m. t = 4 h = 2 . ? J = 1,53 ×2.
4.15. R = 0,5 , m = 10 . , , = 2,04 /2.
4.16. m = 150 R = 6 , 9 . F = 50 , t = 10 . m.
4.17. ( 2 ) V0 = 2 /. F = 5 ? m1 = 3 , m2 = 3 .
4.18. R = 20 J = 0,1 ×2 , m = 0,5 . h = 1 . t ?
4.19. , , φ = At + Bt3, B = 0,2 /3, = 2 /. , τ = 2 . J = 0,048 ×2.
4.20. , m = 0,4 , , m1 = 0,3 m2 = 0,7 . 1 2 .
4.21. R = 0,5 F= 100 . = 2 ×. m , , ε = 12 /2.
4.22. n1 = 300 / n2 = 180 / t = 1 . . J = 2 ×2.
4.23. R = 5 h = 1 = 2 , = 2,5 . , . ρ = 8,9 /3.
4.24. , , m = 2 , = 3 , - R = 5 .
4.25. m = 0,5 , . R = 0,02 , - = 0,01 .
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4.26. , , . m1 = 60 . , , , ? m2 = 240 . , .
4.27. ( , , ) l= 2,4 m = 8 , . ν = 1 -1. , ? J = 6 ×2.
4.28. , R = 2 , m1 = 80 . m2 = 240 . , . , , ω , V = 2 / .
4.29. m1 = 10 m2 = 1 n1 = 10 / , . . n2.
4.30. l = 2 m = 8 . m1 = 10 , V = 800 /. ?
4.31. m = 80 R = 1 n = 20 /. . , , , J1 = 2,94 ×2 J2 = 0,98 ×2? .
4.32. E = 1000 . , N = 80 , . M.
4.33. , J = 4,0 ×2, = 20 ×. t = 10 . , .
4.34. l = 1 , . a = 600 . V .
4.35. l = 85 , . V , ?
4.36. m = 210 l = 1 . . = 3 ×/ l = 20 . w, .
4.37. a , , , V = 5 /? l = 1 .
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4.38. n1 = 14 /. . , n1 = 25 /. m = 70 . M. , .
4.39. m = 80 R = 30 . , n = 10 /? , ?
4.40. l= 15 , , . w V : 1) ; 2) ? .
4.41. V , h = 1 .
4.42. V0 = 12 /. α, l = 2 .
4.43. n = 900 /. N = 75 . A = 44,4 . : 1) J; 2) M.
4.44. , a = 300, V = 7 /, ?
4.45. m1 = 5 R = 5 c, n = 10 /, m2 = 10 . , , . .
4.46. R = 10 m = 2 ν = 2 / , . , ?
4.47. m = 60 ,
l1 = 1,2 , n1 = 2 /. , l2 = 0,6 . n2 ? , ?
4.48. , , . ? .
4.49. n = 10 /, = 7,85 . t = 50 ×, , ?
4.50. ε = 0,5 / t1 = 15 L = 73,5 ×2/. t2 = 20 .
5.
:
x=Acos(wt+j0), x=Asin(wt+j0), ,
x - , A - , wt+j0 - t, w - , j0 - .
u T - .
:
, m - , k - .
, ,
, ( ),
m - , k - .
l - , g - .
J - , a - .
,
c - , d - , - .
( ):
A0 - t=0,
A(t) - t.
T - .
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1. l1=40 l2=60 . a .
,
.
(1)
:
(2)
(2) (1),
(3)
(3) : a1=10 , a2=30 .
, .
(1) .
: a1=10 , a2=30 .
2. , Px x . m1, w0, A.
(1)
(2)
(1) (2) ,
(3)
(4)
(3) (4) . ,
- .
: .
3. , . .
:
j - t, t=0, j=0.
. (1)
(1) t t+t:
, .
. (2)
(2),
.
: t=1,79 .
5.1. Dx = 9 . T .
5.2. , 1/ 2 = 1,5.
5.3. , a = 2,5 /2. T . 1 .
5.4. , , a = 3 /2. T . 1 .
5.5. m , "". . k1 k2.
5.6. m , "". . k1 k2.
5.7. , , . , ?
5.8. l = 30 : - , - . , . T . .
5.9. l = 30 m = 1 , : - , - . , . T .
5.10. R = 20 , . n .
5.11. m l , . .
5.12. m, l , l/4 . .
5.13. 200 , 500 /. 10 , 300 /, . . , .
5.14. 0,5 l , . 10 , 300 /, . .
5.15. , 1/4 . 10 , 200 /, . . 0,5 , 1 .
5.16. 5 2. 8 ?
5.17. 1 . 10 2 . .
5.18. m, k, . 9. 2 ? ?
5.19. l φ1 φ2, φ2 <φ1 << 1. .
5.20. . : a1 = 560 , a2 = 440 , a3 = 520 . ? .
5.21. Fx = F0cos(ωt) m, k, . , .
5.22. ? , β ≥ ω0 / ?
5.23. β1 < β2 < β3 .
5.24. . : 1) ; 2) .
5.25. 4,45×1014 , 2,32×10-26 . , .
5.26. , , = Asinω(t + τ), ω = 2,5 π-1, τ = 0,4 , - .
5.27. = Acos(ωt + φ), = 2 , ω = π -1, φ = π/4 . , .
5.28. : = 4 , = 2 . . (0) = 0, (0) < 0.
5.29. = 6 . d = 20 . . , t = 0 (0) = 0. , t = 1 .
5.30. . ?
k - ; A - ; m - ; ω - ; x - ; V - ; Fmax -
5.31. . : , , , , ?
5.32.
= Acos(ωt), = 5 , ω = 2 -1.
, 8 /.
5.33. φ = φ0sin(ωt + ). φ1 = 0,1 π, . .
5.34. = 7sin0,5πt. ?
5.35. , = 2 , max = 49,3 /2, (0) = 25 .
5.36. m = Acos(ωt + π/4) : T(t), u(t), E(u), T(u), T(x) u(x). , u, E - , .
5.37. = Asin(ωt + φ0). φ0 t = 0.
5.38. t0 = 0 t1 = π /2ω : ) = Acos(ωt + π/4), ) = 2Acos(ωt- -π/6). > 0.
5.39. = Acosωt, = 8 , ω = 2π/3 . , , , 5 , 100 . .
5.40. 103 . , 998 .
5.41. m k F = F0sin(ωt). F0, ω, m k? , ?
5.42. x = Asin(ωt). , x1 =2,4 V1 = 3 /. , x2 = 2,8 , V2 = 2 /. .
5.43. m = 10 = Asin(πt/5 + π/4), = 5 . , , .
5.44. . , Vmax = 10 c/, amax = 100 /2. .
5.45. . , xmax = 10 , Vm = 20 /c. .
5.46. x = Asin(ωt). 1 5 . 2, 2 = 8. .
5.47. x = Asin(ωt), = 10 , ω = 5 . : 1) ωt = π/3; 2) .
5.48. n1 = 200 n2 = 300 . , .
5.49. : n1 = 20,0; n2 = 5,6 n3 = 12,8. , , .
5.50. , ? 1 , 0,002.
I
0 1.11 1.27 2.11 2.26 3.11 3.37 4.11 4.36 5.1 5.26 1 1.12 1.28 2.12 2.27 3.12 3.38 4.12 4.37 5.2 5.27 2 1.13 1.29 2.13 2.28 3.13 3.39 4.13 4.38 5.3 5.28 3 1.14 1.30 2.14 2.29 3.14 3.40 4.14 4.39 5.4 5.29 4 1.15 1.32 2.15 2.30 3.15 3.41 4.15 4.40 5.5 5.30 5 1.16 1.33 2.16 2.31 3.16 3.42 4.16 4.41 5.6 5.31 6 1.17 1.38 2.17 2.32 3.17 3.43 4.17 4.42 5.7 5.32 7 1.18 1.39 2.18 2.33 3.18 3.44 4.18 4.43 5.8 5.33 8 1.19 1.40 2.19 2.34 3.19 3.45 4.19 4.44 5.9 5.34 9 1.20 1.41 2.20 2.35 3.20 3.46 4.20 4.45 5.10 5.35 |
1. .. . - .: , 1979.
2. .., .. . - : . ., 1989.
3. . . .:, 1989.
4. .., .. . : , 1994.
5. .. . - .: , 1988.
6. .. . .1. . - .: , 1989.
7. .. . .1. . - .: , 1989.
8. .. . - .: , 1975.
9. .. . . . - .: . ., 1989.
10. .. . - .: . ., 1978.
11. .., .. . - .: . . 1981.
12. .., .. . - .: , 1980.