The CAT rating required for a test instrument used outdoors.

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Chapter 3.2, Problem 5CP

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The CAT rating required for a test instrument used outdoors.

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4. Answer the following questions. Take help from ChatGPT to answer these questions (if you need). But write the answers briefly using your own words with no more than two sentences and make sure you check whether ChatGPT is giving you the appropriate answers in our context. A) What is the zero-input response? B) What is the zero-state response? C) What are pole, zero, and residue in the context of our class? D) What are the different methods for finding the inverse Laplace transform? Which one we used in this class?

3. You have come to encounter an LTI system. You have no idea how the system behaves. So, you decide to drive the system with a particular input and measure the output. When you put the input u(t) = et 1(t), you find that the output y(t) = (1-e) 1(t). You can assume zero initial conditions. Now, find the transfer function of the system.

1. Consider the following LTI system. d²y dy du +7 +6y= -- +2u, t≥0 dt² dt dt a) What is the impulse response of the system? Recall, h(t) = L-¹(H(s)). b) What are poles and zeros of the system? c) Suppose the initial condition of the system is y(0) = 1 and y'(0) = 4. What is the zero-input response of the system? d) Consider an input u(t) = (1 + et) 1(t) to the system. What is the zero-state response of the system for this input? e) Suppose, the initial condition was y(0) = -2 and y'(0) = -8 and the input is u(t)=(1+e) 1(t). What will be the total response of the system? You should be able to answer this using the linearity property of the system and your answers in part b and part c without taking any inverse Laplace transform.