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I am doing an experiment which includes looking at how the damping constant is affected when you attach circular disks with different surface area to a spring mass system. It is also submerged in a beaker filled with water. In order to obtain the best raw data I had to use a force sensor instead of a motion detector and now I am having trouble with my calculations.

(Damping is not part of my curriculum, so I have had to learn about it independently)

In Logger Pro I have the option to "Damped Harmonic" curve fit, but I have only seen those equations with amplitude vs time graphs, not force vs time. Is it possible to use this curve fit in order to find the damping coefficient?

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If not, are there any calculations I can do with this data that can create a graph with the surface area of the disks on the x-axis and some other value on the y-axis?

Thank you :)

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Let's take the equation of motion : \begin{equation} m \dfrac{d^2x}{dt^2} + \gamma\dfrac{dx}{dt} + \omega_0^2 x = 0 \end{equation}

The damping coefficient is thus $\gamma$. The solution for the motion of an under-damped oscillator follows (assuming $x=0$ at equilibrium) : \begin{equation} x(t) = \lambda e^{-\gamma t/2m}\cos (\omega t+\phi) \end{equation} The force is $F=m\dfrac{d^2x}{dt^2}$, so it is proportional to the second derivative of $x$. Derivating $x$ will not affect the argument of the exponential, and so this argument will still be $-\gamma t$ in each exponential in the resulting expression of $F$. As a result, the value of $B$ in your fit parametrization should be equal to $\gamma$. The same reasoning applies to the cosine function : the force will oscillate at the same frequency as the mass attached to the spring. The oscillation pulsation won't be exactly $\omega_0$, but rather : \begin{equation} \omega = \omega_0\sqrt{1-\dfrac{\gamma^2}{4m^2\omega_0^2}} \end{equation}

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