Classtest1ae21008_quespaper.docx

INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR Date 07/02/2019, Time: 50 min Full Marks: 30 , Aerospace Engineering Department No. of Students 54, Class Test I Introduction to Flight Vehicle Controls (AE21008)

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1) Find the unity feedback system that is equivalent to the system shown in Fig. 1.

Figure 1 2) a) A spring-mass system with mass 2, damping 4, and spring constant 10 is subjected to a hammer blow at time t = 0. The blow imparts a total impulse of 1 to the system, which was initially at rest. Find the response of the system. b) A unit impulse is applied to the mass in a spring-mass-damper system, initially at equilibrium, and you observe the system respond as x(t) = e−2t sin(5t). What are the physical parameters mass, damping coefficient and spring constant? 3) (a) A system is described by the following differential equation. 𝑑2𝑥 𝑑𝑥 + 2 + 3𝑥 = 1 𝑑𝑡 2 𝑑𝑡 with the initial conditions 𝑥(0) = 1, 𝑥̇ (0)= −1. Show a block diagram of the system, giving its transfer function and all pertinent inputs and outputs. (b) Find the transfer function 𝐺(𝑠) = 𝑥2 (𝑠)/𝐹(𝑠), for the translational mechanical system shown in the following figure.