As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the spring constant at time $t$ is $k(t)=t*sin(\frac{t}{100})\frac{N}{m}.$ If the mass$-$spring system has mass $m=2kg$ and a damping constant $b=1N-s\frac{ec}{m}$ with initial conditions $x(0)=6m$ and $x^{\text{'}}(0)=-5\frac{m}{sec}$ and it is subjected to the harmonic external force $f(t)=100*cos3tN.$ Find at least the first four nonzero terms in a power series expansion about $t=0,$ i$.$e$.$ Maclaurin series expansion, for the displacement:

Analytically $($hand calculations$)$

Creating Simulink Model

Plot solutions for first two, three and four non$-$zero terms as well as the Simulink solution on the same graph for the first $15$ sec $.$ The graph must be fully formatted by code.