$(\frac{?}{{?}_5}$ points$)$:

Given the equation of motion of a dynamic system:

$2x^{}+4x^{}+8x=f$

Answer the following questions.

What is the degree of freedom of the system? $(2$ pts$)$

Is this a conservative $($lossless$)$ system? $(1$ pts$)$ Why? $(2$ pts$)$

What are $m_{eq},k_{eq}$ and $c_{eq}$ respectively for this system? $(3$ pts$)$

Calculate the natural frequency ${}_n(3$ pts$)$

Calculate the damping ratio $(3$ pts$)$ Is it overdamping, underdamping or critical damping? $(2$ pts$).$

Assuming $f=0,$ express the solution $x(t)(2pts).$ What are the unknowns in this solution? $(2$ pts$)$ How the unknowns can be solved? $(2$ pts$)$

When there is an external force acting on the mass $)(0,$ how the solution $x(t)$ is different compared to when there is no external force? $(3$ pts$)$