Problem $3.$ The spring$-$mass system below includes a particle with mass $m=5kg$ attached to

two springs with stiffness of $5\frac{N}{m}$ and $10\frac{N}{m}.$ If the mass had the initial conditions: $x(0)=$

$0\mathrm{.}2$ m and $x^{}(0)=0\mathrm{.}1\frac{m}{s},$ answer the following questions:

a$.$ Find the equation of motion $($EOM$)$ of the spring$-$mass system.

b$.$ Find the natural frequency of the system.

c$.$ Find $x(t).$

d$.$ Find the amplitude and phase of the vibration.

e$.$ Find the maximum amplitude of velocity and acceleration of vibration.

f$.$ Plot $x(t).$ In the plot, clearly identify the amplitude, the phase, the point$($s$)$ of maximum

velocity.