Suppose a spring with spring constant $3 \ \mathrm{N/m}$ is horizontal and has one end attached to a wall and the other end attached to a $3 \ \mathrm{kg}$ mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is $6 \ \mathrm{N \cdot s / m}$.

1. Set up a differential equation that describes this system. Let $x$ to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of $x, x^{\,\prime}, x^{\,\prime\prime}$. Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium.
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2. Find the general solution to your differential equation from the previous part. Use $c_1$ and $c_2$ to denote arbitrary constants. Use $t$ for independent variable to represent the time elapsed in seconds. Enter $c_1$ as c1 and $c_2$ as c2.
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3. Is this system under damped, over damped, or critically damped? ? over damped critically damped under damped Enter a value for the damping constant that would make the system critically damped.
   $\mathrm{N \cdot s / m}$ help (numbers)