(Solved): A mass-spring-dashpot system with external force f(t) is described by the following differential eq ...

A mass-spring-dashpot system with external force f(t) is described by the following differential equation. \[ m x^{\prime \prime}+c x^{\prime}+k x=f(1) \] \( m=1, k=36, c=0 ; f(t) \) is a square-wave function with amplitude 5 and period \( \frac{2 \pi}{3} \). Under the assumption that \( x(0)=x(0)=0 \), use a series representabion of \( F(s) \) to find the transient and steady periodic motions of the mass. Then construct the graph of the position function \( x(t) \). If you would like to check your graph using a numerical DE solver, 4 may be useful to note that the function \( \mathrm{ft} \mathrm{t} \), shown below, has the value \( +\mathrm{A} \) if \( 0