# Differential calculus, physics problem

1. Feb 21, 2015

### dlp248

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. Feb 21, 2015

### SteamKing

Staff Emeritus
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".

3. Feb 22, 2015

### dlp248

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!