GR8677 #77



Alternate Solutions 
ethanque 20150812 08:54:41  Hooke's Law and Work Energy Theorem:
I couldn't remember my wave equations right away so I used the work energy theorem imagining this is a SHO/spring:
The particle has zero kinetic energy when , and it is subject to the force as it travels from to . i.e. the spring does work on the particle.
So, integrate
Recall that . Then
Recall that . Then
, which is option (B).
Baddabing baddaboom!   wittensdog 20091007 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 20080807 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.   rreyes 20051031 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 20051101 02:14:55 
fyi, add in dollarsign wrappers around the equations in your comments... and the system processes your latexcompatible syntax into niftylooking equations.
quote rreyes:
an alternative solution is conservation of energy
plugging in gives

nitin 20061116 13:32:49 
Thumbs up mate!

 

Comments 
ethanque 20150812 08:54:41  Hooke's Law and Work Energy Theorem:
I couldn't remember my wave equations right away so I used the work energy theorem imagining this is a SHO/spring:
The particle has zero kinetic energy when , and it is subject to the force as it travels from to . i.e. the spring does work on the particle.
So, integrate
Recall that . Then
Recall that . Then
, which is option (B).
Baddabing baddaboom!
ethanque 20150812 08:58:27 
WOW! My solution looked fine in the preview. Sorry, for that jumbled mess of latex jargon... help?

yosun2015 20150823 06:22:33 
fixed! :)

  tpatt 20110905 14:08:10  Can someone explain why (omega*t + phi) = pi/6? I'm not following that step.
livieratos 20111108 06:03:21 
cause then sin(omega*t + phi) = sin(pi/6) = 1/2 as was given...

  anum 20101111 11:37:29  v=r*w =2*pi*f*A putting in A/2 in place of A gives v=pi*f* A . but its not correct; can anyone tell why?
IRFAN 20110818 03:19:30 
this velocity you have determin works only at particular point,in next you find the velocity of a different motion wich have halv the amplitrude

  shafatmubin 20091102 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 20091007 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 20080807 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 20080807 13:09:33 
"Another way to solve the problem is" ....

  rreyes 20051031 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 20051101 02:14:55 
fyi, add in dollarsign wrappers around the equations in your comments... and the system processes your latexcompatible syntax into niftylooking equations.
quote rreyes:
an alternative solution is conservation of energy
plugging in gives

nitin 20061116 13:32:49 
Thumbs up mate!

zeper 20130324 11:59:00 
that is the best one....;)

 




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