(Solved): A spring-mass-damper system (damped harmonic oscillator) is constrained to move horizontally as sho ...

A spring-mass-damper system (damped harmonic oscillator) is constrained to move horizontally as shown below. An input force $f(t)$ is applied to the mass. The displacement $x$ is measured from the undeformed position of the spring and is positive when directed to the right. In previous work, the equation of motion for the system was determined $m\ddot{x}+b\stackrel{?}{x}+kx=f(t)$ The mass is $m=9\mathrm{kg}$, the damping coefficient is $b=99\mathrm{N}?\mathrm{s}/\mathrm{m}$ and the spring constant is $k=252\mathrm{N}/\mathrm{m}$. The system has initial conditions $x(0)=5\mathrm{m}$ and $x(0)=45\mathrm{m}/\mathrm{s}$ and the input is zero: $f(t)=0$ Save your answer offline because you will be asked to plot and analyze your solution in MATLAB in the following nodes. Find the system response $x(t)$ using Laplace transforms and enter it below. Use fractional form for your answers. Units are given.