Calculate the following values for the system shown.

a$)$ The equivalent damping constant, $c_{eq},$ equivalent stiffness, $k_{eq},$ and equivalent mass, $m_{eq}?$

b$)$ The un$-$damped natural frequency, ${}_n?$

c$)$ The critical damping constant, $c_c?$

d$)$ The damping ratio, $.$

e$)$ The logarithmic decrement, $.$

f$)$ The damped natural frequency, ${}_d?$

g$)$ The energy dissipated per cycle, $E_d.$

h$)$ The governing differential equation