anonymous
  • anonymous
A spring hanging from the ceiling vibrates up and down. it's vertical position at time (t) is given by f(t)=4 sin(3t). (a) Find the velocity of the spring at time t. (b) What is the spring's maximum speed. (c) what is location when it reaches its maximum speed.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
You know that the position as a function of time is: \[x(t) = 4\sin(3t)\] you also know that velocity is defined as: \[\frac{dx}{dt}\]
anonymous
  • anonymous
can you find the derivative of: \[x(t) = 4\sin(3t)\]
anonymous
  • anonymous
Yes that is the ans of a.what about b and c parts?

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anonymous
  • anonymous
so we want to find the maximum of: \[12\cos(3t)\]
anonymous
  • anonymous
So this basically comes down to finding where the cosine function has it's maximums
anonymous
  • anonymous
and then using the value for the maximum of a cosine in the equation
anonymous
  • anonymous
So, what is the maximum of a cosine function?
anonymous
  • anonymous
1
anonymous
  • anonymous
yes, so the maximum value for the speed must be:
anonymous
  • anonymous
i think 12
anonymous
  • anonymous
yes
anonymous
  • anonymous
At what time does the speed become 12?
anonymous
  • anonymous
don't know.may be 0
anonymous
  • anonymous
Yes, because cos(x) = 1 when x = 0
anonymous
  • anonymous
Now that you know the time at which it reaches its maximum speed, you can plug that into the first equation
anonymous
  • anonymous
which first equation?
anonymous
  • anonymous
the equation for position as a function of time
anonymous
  • anonymous
f(t)=4sin(3t)
anonymous
  • anonymous
yes
anonymous
  • anonymous
what i do with this now? please explain
anonymous
  • anonymous
i put t=0 so position is zero?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
ok.Thanks a lot.
anonymous
  • anonymous
You are welcome

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