Задача №32.100
Условие
На тело массы 0,4 кг, прикрепленное к пружине с коэффициентом жесткости c=4 кН/м, действуют сила S=40sin50tН и сила сопротивления среды R=-αv, где α=25 Н*с/м, v — скорость тела (v в м/с). В начальный момент тело покоится в положении статического равновесия. Найти закон движения тела и определить значение частоты возмущающей силы, при котором амплитуда вынужденных колебаний будет максимальной.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
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2.9
2.10
2.11
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2.13
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2.25
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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
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2.53
2.54
2.55
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
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3.11
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3.13
3.14
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3.19
3.20
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3.25
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4.1
4.2
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4.4
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4.49
4.50
4.51
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4.53
4.54
4.55
4.56
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4.61
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4.74
5.1
5.2
5.3
5.4
5.5
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6.1
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8.1
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9.1
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9.3
9.4
9.5
9.6
9.7
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9.12
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9.27
10.1
10.2
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10.4
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10.6
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11.1
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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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21.2
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22.1
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23.1
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23.48
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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
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24.31
24.34
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25.1
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26.1
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26.4
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26.6
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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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27.25
27.26
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27.30
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
28.8
28.9
28.10
28.11
28.12
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29.1
29.2
29.3
29.4
29.5
29.6
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30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
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30.10
30.11
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30.13
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30.20
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30.25
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30.27
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30.29
30.30
31.1
31.2
31.3
31.4
31.5
31.6
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31.9
31.11
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31.14
31.15
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31.25
31.26
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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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32.11
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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
32.76
32.77
32.79
32.80
32.81
32.82
32.83
32.84
32.85
32.86
32.87
32.88
32.89
32.90
32.91
32.92
32.93
32.94
32.95
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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33.14
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33.16
33.17
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33.22
34.1
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34.5
34.6
34.7
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34.10
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34.31
35.1
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36.1
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37.1
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37.48
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37.53
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37.59
38.1
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38.53
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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42.4
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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
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45.3
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45.37
46.1
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47.1
47.2
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48.1
48.5
48.6
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48.38
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48.48
48.49
49.1
49.2
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49.11
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53.5
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54.1
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54.32
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54.35
55.2
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56.3
56.7
56.9