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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.
 one year ago
 one year ago
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.
 one year ago
 one year ago

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MrMooseBest ResponseYou've already chosen the best response.1
You know that the position as a function of time is: \[x(t) = 4\sin(3t)\] you also know that velocity is defined as: \[\frac{dx}{dt}\]
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
can you find the derivative of: \[x(t) = 4\sin(3t)\]
 one year ago

FaisalAyazBest ResponseYou've already chosen the best response.0
Yes that is the ans of a.what about b and c parts?
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
so we want to find the maximum of: \[12\cos(3t)\]
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
So this basically comes down to finding where the cosine function has it's maximums
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
and then using the value for the maximum of a cosine in the equation
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
So, what is the maximum of a cosine function?
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
yes, so the maximum value for the speed must be:
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
At what time does the speed become 12?
 one year ago

FaisalAyazBest ResponseYou've already chosen the best response.0
don't know.may be 0
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
Yes, because cos(x) = 1 when x = 0
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
Now that you know the time at which it reaches its maximum speed, you can plug that into the first equation
 one year ago

FaisalAyazBest ResponseYou've already chosen the best response.0
which first equation?
 one year ago

MrMooseBest ResponseYou've already chosen the best response.1
the equation for position as a function of time
 one year ago

FaisalAyazBest ResponseYou've already chosen the best response.0
what i do with this now? please explain
 one year ago

FaisalAyazBest ResponseYou've already chosen the best response.0
i put t=0 so position is zero?
 one year ago
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