Tutorial 4: Systems Modeling and Systems Response Problems Q.1 a) Obtain differential equations for the systems. X(s) b) Obtain transfer functions for the systems F(s) Mass m - Displacement x (a) K, 000 080 000000 - Displacement x (b) Q.2 Obtain differential equations for the system under torsion. (TORQUE APPLIED) Q.3 Assume y is the displacement of mass m from equilibrium position. a) Write the differential equation for y(t). b) Determine the transfer function of Y(s) F(s) F 7 m Instrumentation & Control p. 1 of 4Q.4 The following diagram shows a thermal system involving two compartments with one containing a heater. If the temperature of the compartment containing the heater is I1, the temperature of the other compartment is T2 and the temperature surrounding the compartments is T3. Develop equations describing how the temperatures Ti and T2 will vary with time. All the walls of containers have the same resistance Rt and negligible capacity. The two containers have the same capacity Ct. To Q.5 Identity the open-loop gain and time constant of the following first-order system transfer functions: (a) G (s ) = - 3 s + 10 (b) G, (s ) =- 6 s+ 1 (c) G, (S ) = - 2 s+ 3 Q.6 What is the steady state value of the output from the following systems when a step of magnitude 3 is injected? (a) G, (s) = - 10 2s + 1 (b) G, (s ) = 3 S+ 4 10 (c) G, (S)= 2s + 3 Q.7 Refer the translational system shown in Figure Q1 where x is the displacement Instrumentation & Control p. 2 of 4from equilibrium position, find out: (a) the differential equation between x and f, (b) the Laplace transform of the differential equation, X(s) 5 F(s) (d) X(s)if F(s)=2>, Ki=2N/m, Ko=2N/m, Ks