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