Design a controller for this physical system that utilizes full state-feedback control. you are going to design your controller by using pole-placement method and linear quadratic regulator method. the design criteria for this problem are:
 settling time less than 3 seconds
 overshoot less than 5%

Aspring with a mass of 2 kg has a damping constant 14 kg/s. a force of 3.6 n is required to keep the spring stretched 0.3 m beyond its natural length. the spring is stretched 0.6 m beyond its natural length and then released. find the position of the mass at any time t. (assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.)

Act has a 1200: 5 or 240: 1 turns ratio. it is short circuited. what is the maximum current at 1200a primary if we put a 100ohm resistor across the secondary end of the ct. use it as current source circuit.

The membrane surrounding a living cell consists of an inner and an outer wall that are separated by a small space. assume that the membrane acts like a parallel plate capacitor in which the effective charge density on the inner and outer walls has a magnitude of 7.0 × 10-6 c/m2. (a) what is the magnitude of the electric field within the cell membrane? (b) find the magnitude of the electric force that would be exerted on a potassium ion (k+; charge = +e) placed inside the membrane.