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FaisalAyaz

  • 3 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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  1. MrMoose
    • 3 years ago
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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: \[\frac{dx}{dt}\]

  2. MrMoose
    • 3 years ago
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    can you find the derivative of: \[x(t) = 4\sin(3t)\]

  3. FaisalAyaz
    • 3 years ago
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    Yes that is the ans of a.what about b and c parts?

  4. MrMoose
    • 3 years ago
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    so we want to find the maximum of: \[12\cos(3t)\]

  5. MrMoose
    • 3 years ago
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    So this basically comes down to finding where the cosine function has it's maximums

  6. MrMoose
    • 3 years ago
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    and then using the value for the maximum of a cosine in the equation

  7. MrMoose
    • 3 years ago
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    So, what is the maximum of a cosine function?

  8. FaisalAyaz
    • 3 years ago
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    1

  9. MrMoose
    • 3 years ago
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    yes, so the maximum value for the speed must be:

  10. FaisalAyaz
    • 3 years ago
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    i think 12

  11. MrMoose
    • 3 years ago
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    yes

  12. MrMoose
    • 3 years ago
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    At what time does the speed become 12?

  13. FaisalAyaz
    • 3 years ago
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    don't know.may be 0

  14. MrMoose
    • 3 years ago
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    Yes, because cos(x) = 1 when x = 0

  15. MrMoose
    • 3 years ago
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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

  16. FaisalAyaz
    • 3 years ago
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    which first equation?

  17. MrMoose
    • 3 years ago
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    the equation for position as a function of time

  18. FaisalAyaz
    • 3 years ago
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    f(t)=4sin(3t)

  19. MrMoose
    • 3 years ago
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    yes

  20. FaisalAyaz
    • 3 years ago
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    what i do with this now? please explain

  21. FaisalAyaz
    • 3 years ago
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    i put t=0 so position is zero?

  22. MrMoose
    • 3 years ago
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    Yes

  23. FaisalAyaz
    • 3 years ago
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    ok.Thanks a lot.

  24. MrMoose
    • 3 years ago
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    You are welcome

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