(Solved): 1. Given the following schematic of a simple mechanical system where the mass, \( M=1 \mathrm{~kg} ...

1. Given the following schematic of a simple mechanical system where the mass, \( M=1 \mathrm{~kg} \), damping coefficient, \( b=5 \mathrm{Ns} / \mathrm{m} \), spring constant, \( \mathrm{k}=4 \mathrm{~N} / \mathrm{m} \) and applied force \( F=F(t)=0.4 \mathrm{~N} \), draw the FBD and provide the system model (ordinary differential equation) describing the system (please note that displacement, \( x \), is absolute for this schematic). 2. At equilibrium, the mass has moved how far to the left from its initial position? Please briefly show your work. a) \( 10 \mathrm{~m} \) b) \( 1 \mathrm{~m} \) c) \( 0.1 \mathrm{~m} \) d) Insufficient information provided e) I used to know how to do this f) I have no idea 3. The general form of the solution for the model (ordinary differential equation) describing this system is (note that the system is initially at rest) a) \( k_{1}+k_{2} e^{-t}+k_{3} e^{-4 t} \) meters b) \( k_{1}+k_{2} e^{-2 t} \cos (t)+k_{3} e^{-2 t} \sin (t) \) meters c) \( k_{1}+k_{2} e^{-t} \cos (2 t)+k_{3} e^{-t} \sin (2 t) \) meters d) None of the above e) Insufficient information provided f) I used to know how to do this g) I have no idea