$1-2$ System B shows a spring$-$damper system. Parameters for the spring, damper, and mass are $k_1=2100\frac{N}{m},b_2=1300N**\frac{s}{m},$ and $m_3=150kg.$ The spring has an initial compression of $0\mathrm{.}025$ m $.$ Note: A compression of $0\mathrm{.}025$ m corresponds to an initial displacement $x_0=-0\mathrm{.}025m.$ The initial velocity of the mass is $0\mathrm{.}03\frac{m}{s}.$ Analyze System B with the following steps:

f$)(4$ pts$)$ Write force balance, geometric continuity, and constitutive equations.

g$)(4$ pts$)$ Obtain differential equations of motion for the extension of the spring and the velocity of the mass.

h$)(6$ pts$)$ Simulate this system with the timestep $dt=0\mathrm{.}01$ seconds for a total of $3$ seconds using the forward Euler method in MATLAB. Plot the extension$/$displacement of the spring and the velocity of the mass as a function of time in separate graphs. Be sure to include axis labels with units.

i$)(2$ pts$)$ Explain the trend in the velocity of the mass as a function of time.