5. A continuous-time system is given by the input/output differential equation d²y(t) dy(t) dx(t) +2- + 3y(t) = + x(t − 2) - dt² dt dt (a) Compute the transfer function H(s) of the system. (b) Compute the impulse response h(t). (c) Compute the step response.

Please help me with this problem and if you could explain each section (a, b, c etc) that would be great. Thank you!

3. For the block diagram below, a. Find the closed loop transfer function b. Find the poles and tell the natures of damping of the closed loop system c. Based on the transfer function, please write down the time domain differential equations between inputs and outputs d. For step input, calculate %OS and R(s) + 10 s(s+2) C(s) - wn, S. Tp. T:

Please provide help with the following as well: (b) Plot the poles and zeros of the system in part (a) (c) Is the system BIBO stable or not? Why?