The following figure is used for problems 1-3.
1. (20 points) A spring-mass-damper system, seen above, has a spring stiffness of $k = 3000$ N/m, damping constant $c = 3000$ N-s/m, and a mass $m = 7.5$ kg. Determine the position of the mass when time $t = 1.1$ s if $x_0 = 1.6$ mm. Is there harmonic motion?
2. (20 points) A spring-mass-damper system, seen above, has a spring stiffness of $k = 3000$ N/m, damping constant $c = 30$ Ns/m, and a mass $m = 7.5$ kg. Determine the position of the mass when time $t = 1.1$ s if $x_0 = 1.6$ mm. Is there harmonic motion?
3. (20 points) A spring-mass-damper system, shown above, has a spring stiffness of $k = 3000$ N/m, damping constant $c = 300$ Ns/m, and a mass $m = 7.5$ kg. Determine the position of the mass when time $t = 1.1$ s if $x_0 = 1.6$ mm. Is there harmonic motion?