Задача №37.23
Условие
Твердое тело, подвешенное на упругой проволоке, совершает крутильные колебания под действием внешнего момента mвz=m0cospt, где m0 и p — положительные постоянные, а z — ось, направленная вдоль проволоки. Момент сил упругости проволоки mупрz=-cφ, где c — коэффициент упругости, а φ — угол закручивания. Момент инерции твердого тела относительно оси z равен Jz. Силами сопротивления движению пренебречь. Определить уравнение движения твердого тела в случаях: 1)√(c/Jz)≠p, 2)√(c/Jz)=p, если в начальный момент при ненапряженной проволоке твердому телу была сообщена угловая скорость ω0.Решение
☆
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1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
2.19
2.20
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.30
2.31
2.32
2.33
2.34
2.35
2.36
2.37
2.38
2.39
2.40
2.41
2.42
2.43
2.44
2.45
2.46
2.47
2.48
2.49
2.50
2.51
2.52
2.53
2.54
2.55
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
3.27
3.28
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3.31
3.32
3.33
3.34
3.35
3.36
3.37
3.38
4.1
4.2
4.3
4.4
4.5
4.6
4.7
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4.10
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4.13
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4.20
4.21
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4.44
4.45
4.46
4.47
4.49
4.50
4.51
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4.53
4.54
4.55
4.56
4.57
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4.59
4.61
4.62
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4.65
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4.74
5.1
5.2
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5.4
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5.42
6.1
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8.1
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9.1
9.2
9.3
9.4
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9.27
10.1
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10.4
10.5
10.6
10.7
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10.23
11.1
11.2
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12.1
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13.1
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14.1
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15.1
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16.1
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17.1
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18.1
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19.1
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20.1
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20.13
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21.2
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22.1
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23.1
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23.44
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23.46
23.47
23.48
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23.55
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23.57
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23.60
23.61
23.62
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23.64
23.65
23.66
23.67
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23.69
23.70
23.71
24.1
24.2
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24.34
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24.46
25.1
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26.1
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26.33
26.34
26.35
27.1
27.2
27.3
27.4
27.5
27.6
27.7
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27.10
27.11
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27.26
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27.28
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27.32
27.33
27.34
27.35
27.36
27.37
27.38
27.39
27.40
27.41
27.42
27.43
27.44
27.45
27.46
27.47
27.48
27.49
27.50
27.51
27.52
27.54
27.55
27.58
27.59
27.60
27.61
27.62
27.63
27.64
27.65
28.1
28.2
28.3
28.4
28.5
28.6
28.7
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29.1
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30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
30.9
30.10
30.11
30.12
30.13
30.14
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30.20
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30.22
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30.24
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30.29
30.30
31.1
31.2
31.3
31.4
31.5
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31.14
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31.20
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31.25
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31.30
31.31
31.32
31.33
31.34
31.35
32.1
32.2
32.3
32.4
32.5
32.6
32.7
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32.10
32.11
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32.13
32.14
32.15
32.16
32.17
32.18
32.19
32.20
32.21
32.22
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32.24
32.25
32.26
32.27
32.28
32.29
32.30
32.31
32.32
32.33
32.34
32.35
32.36
32.37
32.38
32.39
32.40
32.41
32.42
32.43
32.44
32.45
32.46
32.47
32.48
32.49
32.50
32.51
32.52
32.53
32.54
32.55
32.56
32.57
32.58
32.59
32.60
32.61
32.62
32.63
32.64
32.65
32.66
32.67
32.68
32.69
32.70
32.71
32.72
32.73
32.74
32.75
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32.77
32.79
32.80
32.81
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32.84
32.85
32.86
32.87
32.88
32.89
32.90
32.91
32.92
32.93
32.94
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32.96
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32.98
32.99
32.100
32.101
32.102
32.103
32.104
32.105
32.106
32.107
33.1
33.2
33.3
33.4
33.5
33.6
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33.12
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33.22
34.1
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34.6
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34.31
35.1
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35.3
35.4
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36.1
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37.1
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37.59
38.1
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38.38
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39.1
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40.1
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41.1
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42.1
42.2
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42.6
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43.1
43.2
43.3
43.4
43.6
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44.1
44.2
44.3
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45.3
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46.1
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46.32
47.1
47.2
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47.4
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47.6
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48.1
48.5
48.6
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48.12
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48.19
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48.28
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48.31
48.33
48.34
48.35
48.38
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48.41
48.42
48.43
48.44
48.48
48.49
49.1
49.2
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49.11
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53.5
53.12
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54.1
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54.32
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55.2
55.3
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55.38
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56.3
56.7
56.9