Homework Mathematical Modelling 1. Obtain mathematical models of the mechanical systems shown in Figures (1 and 2). ki 3 wr M *(Output) w ki ka u(1) (Input force) 2 M2 No friction (b) Figure (1) Figure (2) 2. Obtain the transfer function Y(s)/U(s) of the system shown in Figure 3. The input u is a displacement input. m2 WW b . 3. Obtain the transfer function X(s)/U(s) and X,(s)/U(s) of the mechanical system shown in Figure 4. 11 ki kz k2 mi m2 bi b2 Figure (4) 4. Write down the mathematical model and Draw the block diagram then Obtain the transfer function V.(S)/V(s) of the electrical systems shown in Figure (5). Where V (s) denotes the input voltage and Vo(s) denotes the output voltage. C R llll C2 He Figure (5) 5. Consider the liquid-level control system shown in Figure (6). Derive a mathematical model for the following system and find the transfer function between the output flow q2 and input flow q. etq Tank 1 Tank 2 Hith R H2h2 R2 7+92 С 0 +91 C2 Figure (6) 6. Consider the liquid-level control system shown in Figure (7).The controller is of the proportional type. The set point of the controller is fixed. Draw a block diagram of the system, assuming that changes in the variables are small. Obtain the transfer function between the level of the second tank and the disturbance input a Proportional controller 0+41 RI с +90 R2 C2 Figure (7)

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