Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the dynamic pull-in instability in a mass-spring model of
  electrostatically actuated MEMS devices   In this work we study the mass-spring system \begin{equation} \ddot x +
\alpha \dot x + x = - \frac{\lambda} {(1+x)^{2}}, \label{e:inertia}
\end{equation} which is a simplified model for an electrostatically actuated
MEMS device. The static pull-in value is $\lambda^{*}=\frac{4}{27}$, which
corresponds to the largest value of $\lambda$ for which there exists at least
one stationary solution. For $\lambda > \lambda^{*}$ there are no stationary
solutions and $x(t)$ achieves the value $-1$ in finite time: {\it touchdown}
occurs. We establish the existence of a dynamic pull-in value
$\lambda_{d}^{*}(\alpha) \in (0, \lambda^{*})$, defined for $\alpha \in
[0,\infty)$, which is a threshold in the sense that $x(t)$ approaches a stable
stationary solution as $t \to \infty$ for $0 < \lambda <
\lambda_{d}^{*}(\alpha)$, while touchdown occurs for $\lambda >
\lambda_{d}^{*}(\alpha)$. This dynamic pull-in value is a continuous, strictly
increasing function of $\alpha$ and $\lim_{\alpha\to\infty}
\lambda_{d}^{*}(\alpha)= \lambda^{*}$.

20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph