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 2 years 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.
 2 years 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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