Q1. A mechanical system is shown in the following figure, where external force u₁ is the input and displacement y₂ is the output. The force acting on m₂ has a linear relationship with u₁ as u₂=Au₁. • List system equations and do Laplace transform to the system equations; • Draw block diagram of the control system. (Please construct the block diagram from system equations directly, do not derive or combine the equations. Do not need to reduce it)

4) Consider the system below. Write the equation of motion and calculate the response assuming that the system is initially at rest for the values k₁ 100[N/m], k2= 100[N/m], k3 = 200[N/m], 100[N/m], k5 = 50[N/m], k6: 50[N/m], and m = = [10kg]. Solve the equation of motion k4 = as a differential equation = F(t) = 80 cos (20t) K5 Κι www K3 ΚΑ m www K6 K2

The ratio of output to input of a system in Laplace domain is known as Transfer function . Select one: True False

1. Find the transfer function. A = [² = ₁], B = [1] . C = [0_1], D = F2] SEST-AT Y(s) U(s) = C[sl-A] B+D X = AY + Bui V = Cx + Du