1. (25%) Consider the following three dynamic systems. (a) Convert the following systems to state-space form....

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1. (25%) Consider the following three dynamic systems. (a) Convert the following systems to state-space form. You only need to find the state equation and not the output equation. (i.e. just write = Az + Bu with A and B populated) (b) Is the first system overdamped, critically damped, or underdamped? dy 2 at - 1 x = f(t) x- 4y+ z = U **-2x-4x= u 3y+ 6x-3y+ 3z= 0 22-32+ y = u 1. (25%) Consider the following three dynamic systems. (a) Convert the following systems to state-space form. You only need to find the state equation and not the output equation. (i.e. just write = Az + Bu with A and B populated) (b) Is the first system overdamped, critically damped, or underdamped? dy 2 at - 1 x = f(t) x- 4y+ z = U **-2x-4x= u 3y+ 6x-3y+ 3z= 0 22-32+ y = u