4. (25%) Consider this awesome rocket sled. m sled (ms) magnetic levitation (neglect friction) Since the...

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4. (25%) Consider this awesome rocket sled. m sled (ms) magnetic levitation (neglect friction) Since the sled is not in contact with the surface, an accelerometer must be used to measure the sled's motion. The deflection of the mass tells us the system's acceleration which we can integrate to determine the system's velocity. The equations of motion for the system are given below. In the accelerometer, the spring constant is kand the damping coefficient is b. The sled's mass and accelerometer mass are ms and ma respectively. Frame xis the reference frame for the sled and yis the internal reference frame for the accelerometer. d(x + y) dy ma +b +ky = 0 dt dt dx ms = F(t) dt (a) Determine the state-space model for the system. (hint: the system is 2nd order) (b) If the mass in the accelerometer is 1 kg. Mathematically determine valid values for the system parameters b and kif the system is critically damped. 4. (25%) Consider this awesome rocket sled. m sled (ms) magnetic levitation (neglect friction) Since the sled is not in contact with the surface, an accelerometer must be used to measure the sled's motion. The deflection of the mass tells us the system's acceleration which we can integrate to determine the system's velocity. The equations of motion for the system are given below. In the accelerometer, the spring constant is kand the damping coefficient is b. The sled's mass and accelerometer mass are ms and ma respectively. Frame xis the reference frame for the sled and yis the internal reference frame for the accelerometer. d(x + y) dy ma +b +ky = 0 dt dt dx ms = F(t) dt (a) Determine the state-space model for the system. (hint: the system is 2nd order) (b) If the mass in the accelerometer is 1 kg. Mathematically determine valid values for the system parameters b and kif the system is critically damped.