I am coming from the computer science territory and have not a long trace in mechanics. My background in derivation of the system dynamics could be summarized with utilization of the `Lagrange Mechanics` but here is a vague point, with which I have confronted, recently. How does the existence of the the `jerk` term in dynamics of a Mass-Spring-Damper could be justified, where the `Lagrange Dynamics` just computes up to the 2nd derivatives of the generalized parameters?!...

If one considers a dynamic system, which (from left to right) consists of a spring with constant $k_1$, a mass $m$, a damper with constant $c$ and the other spring with constant $k_2$, all connected together, respectively, the derived dynamics of the system would be declared as: (The junction of spring $k_2$ and damper $c$ is massless)

$$
\frac{cm}{k_2} · \frac{d^{3} x}{d t^{3}} +
m  \frac{d^{2} x}{d t^{2}}   +
\left(c  + \frac{k-1}{k_2}\right) \frac{dx}{dt}+
k_1 x= 0
$$

Obviously, the `Jerk` term has been appeared, up there, noticeably. 

Would you please guiding me that how such dynamics could be interpreted by either `Lagrange Dynamics` or `Newtonian Method`?!

Thanks in advance.