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A spring-mass system has a spring constant of $\displaystyle\frac{3N}{m}$. A mass of $2$ kg is attached to the spring, and the motion takes place in a viscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an external force of $(3\cos(t)-2\sin(3t))$ N, determine the steady-state response.


My study group came up with the following. Is this reasonable?

$$\begin{align} &k= \displaystyle\frac{3N}{m}\\ &m=\displaystyle\frac{2k}{g}\\ &2y''+ry'+3y=3\cos(3t)-2\sin(3t) \end{align}$$

How do I find $r$?

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    $r$ measures the resistance, right? which is "numerically equal to the magnitude of the instantaneous velocity", right? and the instantaneous velocity is $y'$, right?2011-12-11
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    It would be better to write $k= \displaystyle 3\frac{N}{m}$ and definitely to write $m=2\ kg$ as the first makes the units clear and the second get the k and g in the same place.2011-12-12
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    By the way, I think the symbol $m$ is being used for two different things here. I think $N/m$ stands for newtons per meter, while $m=2{\rm\ kg}$ (and not $m=2k/g$) means mass is two kilograms. But perhaps I misunderstand.2011-12-12

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