24. Find the transfer function, G(s) = X2(s)/F(s), for the translational mechanical system shown in Figure P2.11. (Hint: Place a zero mass at x2(t).) %3D x(1) - x2(1) ft) – 5 kg 10 N/m N-s/m

1. Reduce the following differential equation to the state space equation form. a. y" (t) + 3y' (t) + 2y (t) = u(t) b. y" (t) = u(t) — b₁y' (t) — boy (t) c. 4y" (t) cos (t) y' (t) + sin (t) y (t) = u(t)

Pls help ASAP. Pls show all steps and calculations.

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