Problem $2(2\mathrm{.}5\%)$ Consider the following system as shown. A mass $m_0$ translates along a horizontal

surface. This mass is attached to a disk of mass moment of inertia $J_2$ and radius $r_2$ on the right, and

is attached to a disk at radius $R$ with mass moment of inertia $J_1$ that is attached to a massless disk

of radius $r$ on the left. The disk $J_1$ is linked at the radius $r_1$ to a spring of stiffness $k_1$ that is fixed

on the other end. Meanwhile, the disk on the right is linked to a spring of stiffness $k_2$ that is fixed

on the other end.

$(0\mathrm{.}5\%)$ Determine the kinetic energy of the system with respect to $m0.$

$(0\mathrm{.}5\%)$ Determine the potential energy of the system with respect $m_0.$

$(0\mathrm{.}5\%)$ Determine the effective mass of the system with respect to $m0.$

$(0\mathrm{.}5\%)$ Determine the effective stiffness of the system with respect to $m_0.$

$(0\mathrm{.}5\%)$ Determine the natural frequency of the system with respect to $m_0.$