anonymous
  • anonymous
describe the motion of a point on a wheel that has a centre 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts at its highest point. use y=asink(t-b)+c model or cosine function.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
c=4 and a=.15 ... is that part clear?
anonymous
  • anonymous
a=15 not .15..
anonymous
  • anonymous
false. :) continuing... \[f=\frac{ 1 }{10}\] \[\omega = 2 \pi f\] \[w= \frac{ \pi }{ 5 }\]

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anonymous
  • anonymous
agree so far?
anonymous
  • anonymous
yes i got that part
anonymous
  • anonymous
so the phase...
anonymous
  • anonymous
we want it to be at the highest point when t=0... sin =1 when theta = pi/2 pi/5 *(t-b) = pi/2 pi/5(-b) = pi/2 b= 5/2
anonymous
  • anonymous
\[y = .15 \sin (\frac{ \pi }{ 5} (t+\frac{ 5 }{2})) +4\]
anonymous
  • anonymous
would it be appropriate to keep(t-b) it at pi/5 *(t) + pi/2 ?
anonymous
  • anonymous
you can... that's not the form they ask you to use though...
anonymous
  • anonymous
whoops, should say b=-5/2 up there... typo
anonymous
  • anonymous
oh okay. & also for cosine model it would just be \[y=.15\cos(\frac{ \pi }{ 5 }t) +4\] right??
anonymous
  • anonymous
yes
anonymous
  • anonymous
why would it be -5/2 and not 5/2 ? :S
anonymous
  • anonymous
why is b= -5/2? is that what you're asking?
anonymous
  • anonymous
OH WAIT.. nvm.. you were referring to your reply before the equation. nvm. lol
anonymous
  • anonymous
thanks!
anonymous
  • anonymous
sure:)

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