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GR8677 #77
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Alternate Solutions |
wittensdog
2009-10-07 18:32:43 | Yet another solution...
You can easily find that the argument of the sine function must be 1/2. If you know the value of a sine function at one point, you immediately know the value of cosine, since,
cos^2 + sin^2 = 1 ==>
cos = sqrt ( 1 - sin^2 ) ==>
cos = sqrt(3) / 2
which then you just plug right into the velocity formula. It's similar to the original solution, but you don't need to remember what angles correspond to what values of sine and cosine. |  | lattes
2008-08-07 13:08:18 | Another to solve is: consider Let =A\cos{\omega t}) and =-A\omega\sin{\omega t}) . Squaring both equation and summing them we get: }^{2}+{(\frac{v}{A\omega})}^{2}=1) . Now let  and solve for  . Thus  . (you should remember that  !). A little bit longer solution, but it works. | | rreyes
2005-10-31 08:06:24 | an alternative solution is conservation of energy
1/2kA^2=1/2kx^2+1/2mv^2
plugging in x=A/2 gives
v= \sqrt{3k/4m}A = \sqrt{3}\pi fA
yosun
2005-11-01 02:14:55 |
fyi, add in dollar-sign wrappers around the equations in your comments... and the system processes your latex-compatible syntax into nifty-looking equations.
quote rreyes:
an alternative solution is conservation of energy
plugging in gives
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nitin
2006-11-16 13:32:49 |
Thumbs up mate!
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Comments |
shafatmubin
2009-11-02 10:17:59 | Simple Harmonic Motion flash card:
x = A cos (wt)
v = w Sqrt(A^2 - x^2)
a = -w^2 x
V = (1/2) k x^2 = (1/2) m w^2 x^2
T = (1/2) m v^2 = (1/2) m w^2 (A^2 - x^2) |  | wittensdog
2009-10-07 18:32:43 | Yet another solution...
You can easily find that the argument of the sine function must be 1/2. If you know the value of a sine function at one point, you immediately know the value of cosine, since,
cos^2 + sin^2 = 1 ==>
cos = sqrt ( 1 - sin^2 ) ==>
cos = sqrt(3) / 2
which then you just plug right into the velocity formula. It's similar to the original solution, but you don't need to remember what angles correspond to what values of sine and cosine. | | lattes
2008-08-07 13:08:18 | Another to solve is: consider Let and . Squaring both equation and summing them we get: . Now let and solve for . Thus . (you should remember that !). A little bit longer solution, but it works.
lattes
2008-08-07 13:09:33 |
"Another way to solve the problem is" ....
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| | rreyes
2005-10-31 08:06:24 | an alternative solution is conservation of energy
1/2kA^2=1/2kx^2+1/2mv^2
plugging in x=A/2 gives
v= \sqrt{3k/4m}A = \sqrt{3}\pi fA
yosun
2005-11-01 02:14:55 |
fyi, add in dollar-sign wrappers around the equations in your comments... and the system processes your latex-compatible syntax into nifty-looking equations.
quote rreyes:
an alternative solution is conservation of energy
plugging in gives
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nitin
2006-11-16 13:32:49 |
Thumbs up mate!
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