The transfer function is the ratio of the Laplace transform of the input variable to the Laplace transform of the output variable, with all initial conditions equal to zero. O True O False

• The unity feedback control structure has the following block diagram: w C(s) P(s)

6 Problem Compute the inverse Laplace transform f(t) = L−¹[F(s)] of the following function: s+1 s² + 6s +9 F(s) =

4 rad, = 0.5. On the complex plane, draw the root(s) of a 2nd order system with the following characteristics: W₁ = 4 rad

1. Consider the simplified model we discussed in class about a car on a bumpy road. The car has a mass m supported by stiffness k and damping c. The road gives a displacement excitation R(t) to the car. The transfer function from R(t) to the car displacement y(t) is Hy(s) - Y(s) R(s) cs + k ms² + cs+k (1) (a) Determine the driving point impedance ZR(s), which is the ratio of the velocity R(t) to the force acting on the wheel from the road. (b) Engineer X is testing the car in the Vehicle Dynamics Lab of a start-up company GF.com. Because of insufficient cash flow, Engineer X only has the equipment to mea- sure ZR(s), and identify the zeros and poles of ZR(s). But eigineer X wants to find the poles of Hy(s). To do so, should Engineer X use the zeros or poles of ZR(s) instead? Explain why? m y(t) R(t) Figure 1: A simple model of a car on a bumpy road

Part A and B  SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer for both

I’m am struggling with this question

Use MATLAB to obtain a state model for the following equations; obtain the expressions for the matrices A, B, C, and D. In both cases, the input is f(t); the output: is y. a. 5d³yd²y +7. b. dy +3 dt³ dt² dt Y(s) 5 = F(s) s² +7s+4 - +6y=f(t)

The state z(t) of a dynamical system is solution of equation ż(t) + aż(t) + 25z(t) = 12, with a = 7.3. Calculate the Peak time of the response.

I’m am struggling with this question