(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am asked to write down the equation of motion of [tex]m[/tex] with respect to O, hence show that [tex]x(t)[/tex] satisfies the differential equation.

[tex]m\ddot{x}+r\dot{x}+kx=mg+kl_0+m\ddot{y}[/tex]

See attached diagram.

2. Relevant equations

I have the force of the spring H, the Damping R and the weight W as

[tex]\bold{H}=k(x-y-l_0)\bold{i}[/tex]

[tex]\bold{R}=r\dot{x}\bold{i}[/tex]

[tex]\bold{W}=-mg\bold{i}[/tex]

3. The attempt at a solution

Using the above forces and [tex]\bold{F}=m\ddot{x}[/tex], what I get is

[tex]m\ddot{x}-r\dot{x}-kx=-mg-kl_0-ky[/tex]

I take it I am asked to find the general solution? Where does the [tex]m\ddot{y}[/tex] come from? Do I have the forces correct?

Thanks, James

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# Homework Help: Linear damping model

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