theEric
Hi! I have to find the velocity as a function of displacement for some given force functions.
Here is the question:
Find the velocity \(\dot x\) as a function of the displacement \(x\) for a particle of mass \(m\), which starts from rest at \(x=0\), subject to the following force functions:
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theEric
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One moment!
theEric
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(a) \(F_x=F_0+cx\)
(c) \(F_x=F_0\cos(cx)\)
If I see the general technique, I might be able to get it! Thanks!
Saeeddiscover
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You can use this relation
Saeeddiscover
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|dw:1379923967464:dw|
theEric
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Ah, thank you very much Saeeddiscover!
Saeeddiscover
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Hold on a moment!
theEric
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Okay!
theEric
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Does that work out? Is the \(x\) in \(F_x=F_0+c\large x\) a function of \(t\)?
Saeeddiscover
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For the second one, you may consider this way as well:
|dw:1379924739346:dw|
theEric
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Thank you!
Saeeddiscover
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Please wait a moment. I got a mistake!
theEric
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Okay! If it's in that last part, I can't find it because I don't know that material yet!
Saeeddiscover
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|dw:1379925139264:dw|
Saeeddiscover
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|dw:1379925286166:dw|
theEric
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That all makes sense, thank you!
I'll try to apply those to my problems soon!
theEric
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I think I need to head to bed, though...
theEric
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Thanks again! :)
Saeeddiscover
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Both 1 and 2 you are given simply can be solved using the last equation I gave you. It is true and works properly.
theEric
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Great! I will use that, then! Have a good day!