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mathew0135

  • 3 years ago

A particle moves on a straight line v(t)=sinwt cos ^{3} wt. find the position s(t) if s(0)=0. I've done this style of question before, but the two variables throw me off. I assume that u=cos(wt) but am unsure.

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  1. mathew0135
    • 3 years ago
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    then du=-sin(wt)

  2. mathew0135
    • 3 years ago
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    -du=sin(wt)

  3. mathew0135
    • 3 years ago
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    \[- \int\limits_{?}^{?} (u)^{3} du\]

  4. mathew0135
    • 3 years ago
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    \[-\frac{ 1 }{ 4 } (u)^{4} +c\]

  5. mathew0135
    • 3 years ago
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    \[- \frac{ (coswt)^{4} }{ 4 } +c\] then insert s(0)=0 so..... \[- \frac{ (cosw(0))^{4} }{ 4 } +c\]=0 ... but w is still an unknown...

  6. mathew0135
    • 3 years ago
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    woooooooo no idea whats going on....

  7. mathew0135
    • 3 years ago
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    unless -cosw(0)=0... then c=0... yeah i'm confused, doesn't seem right.

  8. sirm3d
    • 3 years ago
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    \[\mathrm du=-w\cdot\sin wt\,\mathrm dt\]

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