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Homework Help: Differential calculus, physics problem

  1. Feb 21, 2015 #1
    1. The problem statement, all variables and given/known data

    The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber in a car) is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion of a point on such a spring is
    s(t) = 5e^−1.9t sin 2πt
    where s is measured in centimeters and t in seconds. Find the velocity after t seconds. Graph both the position and velocity functions for 0 ≤ t ≤ 2.

    2. Relevant equations

    Chain rule: [f(g(x)]' = f'(g(x))g'(x)
    Product rule: [f(x)g(x)]' = f'(x)g(x) + f(x)g'(x)

    3. The attempt at a solution

    I am stuck finding the velocity function. I believe that I have the correct derivative, however, I am being marked incorrect.

    This is what I have done:

    v(t) = (5e^-1.9t)(-1.9)sin(2πt)+(5e^-1.9t)cos(2πt)(2π)
    v(t) = 5e^-1.9t[-1.9sin(2πt)+2π(cos(2πt)]

    I haven't attempted the rest of the problem because I need the velocity function first.
  2. jcsd
  3. Feb 21, 2015 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    It's not clear why your velocity function is being marked incorrect. Is it due to your work being examined by some computer response system?

    Perhaps submitting a different version of the same function might help. I would try moving the constant 5 inside the [] brackets, leaving the exponential outside by itself.

    I don't have much experience with such systems, but I can see why my late friend called computers "The Devil's Machine".
  4. Feb 22, 2015 #3
    Thanks for getting back to me!

    I was entering this function into a computer for grading. I ended up contacting my professor and she was able to point out to me that the question was asking for a step by step differentiation of the position function. So the velocity function that I found ended up not being needed until part three of the question. Why they do this to us I have no idea!! It is frustrating beyond belief!!! Thank you again!
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