1. Derive a mathematical model for the system of Figure 4 using x, the displacement of the mass center of the disk as the system output. Assume the disk rolls without slip. Fx 2k M(t) No slip Figure 4 2. Derive a mathematical model of the system of Figure 5 using x,,x, and x, the displacements of the masses as the system outputs. k 2k 2k 어 2m m F(t) rond Figure 5 3. Derive a mathematical model of the system of Figure 6 using xando as the system outputs. **** 5L 6 की Slender bar of mass m -Thin disk of mass m, radius T х Figure 6 4. Consider a parallel plate capacitor. Each plate is rectangular and of dimensions 3 mm by 5 mm. A vacuum exists between the plates of the capacitor. (a) If the charge on a plate is 5.2x10SC and the voltage measured across the capacitor plates is 3 V. (1) What is the capacitance of the capacitor? (ii) What is the distance between the plates? (iii) What is the energy stored in the capacitor? (b) If the capacitor used in part a is used in a circuit where the current varies as i(t) = 2.1cos 200 mA and the capacitor is uncharged at t=0.(i) what is the potential difference across the capacitor as a function of time? (ii) What is the energy stored in the capacitor as a function of time? | 5. For the circuit of Figure 8, yn = 30V and v. = 26 V. What are (a) the currents through each wire in the circuit, (b) The potential provided by the source, and (c) the power delivered to the circuit? Vo= 30v Α 4Ω B 302 C 222 D Ve=26v + 702 402 1Ω H 10 G 60 F 30 E Figure 8 6. (a) If y=10 V for the circuit of Figure 9, determine ini, and ij. (b) Replace the resistors by a single resistor of equivalent resistance. 402 302 402 12 202 із 50 402 202 Figure 9 7. (a) Derive the mathematical model for the circuit of Figure 1 using i, i, and i, as outputs and v, and v, as inputs. (b) Draw a mechanical system analogous to the circuit. L, ੪੪੪੪ L2 8888 L3 6868 + Vi R. V2) R2 Ci C3 8. (a) Derive the mathematical model for the circuit shown using in, i, and i, as outputs and V, and v, as inputs. (b) Draw a mechanical system analogous to the circuit. Li 8888 L2 868 Rਤੂ L3 ੪੪੪ + V (V2. R, R2 C2 9. (a) Derive a mathematical model for the mechanical system shown 4 using x,,x2,X, and x, as outputs and F, and F, as inputs. (b) Draw an electrical circuit analogous to this system. Xi > - X2 X3 > X4 ka F1 F2 mi m2 m3 ks kz C3 ॐ