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Math Help - Differential Calc

  1. #1
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    Differential Calc

    The position ( in feet) of an object oscillating up and down at the end of a spring is given by s = A sin [ (square root of ( k/m)) * t ]
    at time t ( in seconds). The value of A is the amplitude of the motion, k is a measure of the stiffness of the spring, and m is the mass of the object. Find the object's velocity at time t.
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  2. #2
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    Velocity would be the derivative of position, so differentiate.

    v(t)=A\cos(\sqrt{\frac{k}{m}}t) \times \frac{d}{dx}\sqrt{\frac{k}{m}}t

    v(t)=A\sqrt{\frac{k}{m}}\cos(\sqrt{\frac{k}{m}}t)
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  3. #3
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    Quote Originally Posted by Jameson
    Velocity would be the derivative of position
    A slight error in terminology.
    This was a distance/speed problem.

    Problems with position/velocity based involved vector function and that is not the case here.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker
    A slight error in terminology.
    This was a distance/speed problem.

    Problems with position/velocity based involved vector function and that is not the case here.
    Speed is intrinsicaly positive, here its velocity because it is signed
    (that is a one dimensional vector).

    RonL
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