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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.

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You know that the position as a function of time is: \[x(t) = 4\sin(3t)\] you also know that velocity is defined as: \[\frac{dx}{dt}\]
can you find the derivative of: \[x(t) = 4\sin(3t)\]
Yes that is the ans of a.what about b and c parts?

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Other answers:

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

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