Harmonisk Oscillator
Vi betragter massen m fastgjort til en fjeder, der p\303\245virker massen via Hooke's lov: 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.
If\303\270lge Newtons anden lov: 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 Lad nu m=2, k=1.
Pkkkb2RlRzYiPCUvLCYtSSVkaWZmRyUqcHJvdGVjdGVkRzYlLUkieUdGJDYjSSJ4R0YkRi9GLyIiIkYsI0YwIiIjIiIhLy1GLTYjRjNGMC8tLUkiREc2JEYqSShfc3lzbGliR0YkNiNGLUY2RjM=
print(); # input placeholder
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print(); # input placeholder
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Vi indf\303\270rer nu d\303\246mpning (gnidningsmodstand): 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. Lad os f\303\270rst antage, at
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEkMC4yRidGOS1GNjYtUSIuRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlcvJStleGVjdXRhYmxlR0Y9Rjk=
Pkklb2RlMkc2IjwlLywoLUklZGlmZkclKnByb3RlY3RlZEc2JS1JInlHRiQ2I0kieEdGJEYvRi8iIiItRik2JEYsRi8jRjAiIiZGLCNGMCIiIyIiIS8tRi02I0Y3RjAvLS1JIkRHNiRGKkkoX3N5c2xpYkdGJDYjRi1GOkY3
print(); # input placeholder
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print(); # input placeholder
LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkSSJmR0YnL0kieEdGJzsiIiEiI1g=
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Bem\303\246rk: Gnidningsmodstand giver d\303\246mpning af svingningen!
Kritisk d\303\246mpning: 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
Pkklb2RlM0c2IjwlLywoLUklZGlmZkclKnByb3RlY3RlZEc2JS1JInlHRiQ2I0kieEdGJEYvRi8iIiIqJi1JJXNxcnRHNiRGKkkoX3N5c2xpYkdGJDYjIiIjRjAtRik2JEYsRi9GMEYwRiwjRjBGNyIiIS8tRi02I0Y7RjAvLS1JIkRHRjQ2I0YtRj5GOw==
print(); # input placeholder
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print(); # input placeholder
LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkSSJmR0YnL0kieEdGJzsiIiEiI1g=
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Vi tilf\303\270jer nu en ekstern (drivende) kraft: 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Lad os betragte det d\303\246mpede tilf\303\246lde igen:
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print(); # input placeholder
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print(); # input placeholder
LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlSSJmR0YnL0kieEdGJzsiIiEiI2wvSSpudW1wb2ludHNHRiciJCsl
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Bem\303\246rk: Indsvingning plus efterf\303\270lgende stabil harmonisk bev\303\246gelse.
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