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FaisalAyaz
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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.
 2 years ago
 2 years ago
FaisalAyaz Group Title
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.
 2 years ago
 2 years ago

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MrMoose Group TitleBest 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: \[\frac{dx}{dt}\]
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
can you find the derivative of: \[x(t) = 4\sin(3t)\]
 2 years ago

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
Yes that is the ans of a.what about b and c parts?
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
so we want to find the maximum of: \[12\cos(3t)\]
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
So this basically comes down to finding where the cosine function has it's maximums
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
and then using the value for the maximum of a cosine in the equation
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
So, what is the maximum of a cosine function?
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
yes, so the maximum value for the speed must be:
 2 years ago

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
i think 12
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
At what time does the speed become 12?
 2 years ago

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
don't know.may be 0
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
Yes, because cos(x) = 1 when x = 0
 2 years ago

MrMoose Group TitleBest 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
 2 years ago

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
which first equation?
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
the equation for position as a function of time
 2 years ago

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
f(t)=4sin(3t)
 2 years ago

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
what i do with this now? please explain
 2 years ago

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
i put t=0 so position is zero?
 2 years ago

FaisalAyaz Group TitleBest ResponseYou've already chosen the best response.0
ok.Thanks a lot.
 2 years ago

MrMoose Group TitleBest ResponseYou've already chosen the best response.1
You are welcome
 2 years ago
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