The following system is oscillating about point O. The link
connecting the spring, damper, and mass elements to this
pivot point is assumed to be massless and rigid.
a) Determine the total kinetic energy of the system in
terms of $\theta$.
b) Determine the total potential energy of the system in
terms of $\theta$.
c) Determine the total dissipated energy of the system
(the Rayleigh's dissipation) in terms of $\dot{\theta}$. Recall that
a linear translational dissipation element has energy
removal defined $D = \frac{1}{2}c\dot{x}^2$.
d) Determine the static equilibrium point $\theta_s$.
e) Based on the findings above, determine $J_e$, $k_e$, and $c_e$ for small oscillations about the static
equilibrium position.
